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

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

module MAlonzo.Code.Algebra.Structures where

import MAlonzo.RTE (coe, erased, AgdaAny, addInt, subInt, mulInt,
                    quotInt, remInt, geqInt, ltInt, eqInt, add64, sub64, mul64, quot64,
                    rem64, lt64, eq64, word64FromNat, word64ToNat)
import qualified MAlonzo.RTE
import qualified Data.Text
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Consequences.Setoid
import qualified MAlonzo.Code.Data.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_IsSuccessorSet'46'constructor_817 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSuccessorSet.isEquivalence
d_isEquivalence_156 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_156 :: T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 T_IsSuccessorSet_146
v0
  = case T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v0 of
      C_IsSuccessorSet'46'constructor_817 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v1
      T_IsSuccessorSet_146
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSuccessorSet.suc#-cong
d_suc'35''45'cong_158 ::
  T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_158 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_158 T_IsSuccessorSet_146
v0
  = case T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v0 of
      C_IsSuccessorSet'46'constructor_817 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSuccessorSet_146
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSuccessorSet._.isPartialEquivalence
d_isPartialEquivalence_162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSuccessorSet_146
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsSuccessorSet_146
v6
  = T_IsSuccessorSet_146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_162 T_IsSuccessorSet_146
v6
du_isPartialEquivalence_162 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_162 :: T_IsSuccessorSet_146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_162 T_IsSuccessorSet_146
v0
  = (T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet._.refl
d_refl_164 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny
d_refl_164 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny
d_refl_164 T_IsSuccessorSet_146
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet._.reflexive
d_reflexive_166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSuccessorSet_146 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSuccessorSet_146
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsSuccessorSet_146
v6 = T_IsSuccessorSet_146
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_166 T_IsSuccessorSet_146
v6
du_reflexive_166 ::
  T_IsSuccessorSet_146 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_166 :: T_IsSuccessorSet_146
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_166 T_IsSuccessorSet_146
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0)) AgdaAny
v1
-- Algebra.Structures.IsSuccessorSet._.sym
d_sym_168 ::
  T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 T_IsSuccessorSet_146
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet._.trans
d_trans_170 ::
  T_IsSuccessorSet_146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 :: T_IsSuccessorSet_146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 T_IsSuccessorSet_146
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet.setoid
d_setoid_172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_172 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSuccessorSet_146
-> T_Setoid_44
d_setoid_172 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsSuccessorSet_146
v6 = T_IsSuccessorSet_146 -> T_Setoid_44
du_setoid_172 T_IsSuccessorSet_146
v6
du_setoid_172 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_172 :: T_IsSuccessorSet_146 -> T_Setoid_44
du_setoid_172 T_IsSuccessorSet_146
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_733
      (T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsMagma
d_IsMagma_176 :: p -> p -> p -> p -> p -> T_Level_18
d_IsMagma_176 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsMagma_176
  = C_IsMagma'46'constructor_1867 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                  (AgdaAny ->
                                   AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMagma.isEquivalence
d_isEquivalence_184 ::
  T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_184 :: T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 T_IsMagma_176
v0
  = case T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0 of
      C_IsMagma'46'constructor_1867 T_IsEquivalence_26
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v1
      T_IsMagma_176
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma.∙-cong
d_'8729''45'cong_186 ::
  T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_186 :: T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 T_IsMagma_176
v0
  = case T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0 of
      C_IsMagma'46'constructor_1867 T_IsEquivalence_26
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMagma_176
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma._.isPartialEquivalence
d_isPartialEquivalence_190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5
  = T_IsMagma_176 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_190 T_IsMagma_176
v5
du_isPartialEquivalence_190 ::
  T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_190 :: T_IsMagma_176 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_190 T_IsMagma_176
v0
  = (T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma._.refl
d_refl_192 :: T_IsMagma_176 -> AgdaAny -> AgdaAny
d_refl_192 :: T_IsMagma_176 -> AgdaAny -> AgdaAny
d_refl_192 T_IsMagma_176
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma._.reflexive
d_reflexive_194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_194 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 = T_IsMagma_176 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_194 T_IsMagma_176
v5
du_reflexive_194 ::
  T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_194 :: T_IsMagma_176 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_194 T_IsMagma_176
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0)) AgdaAny
v1
-- Algebra.Structures.IsMagma._.sym
d_sym_196 ::
  T_IsMagma_176 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_196 :: T_IsMagma_176 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_196 T_IsMagma_176
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma._.trans
d_trans_198 ::
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_198 :: T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_198 T_IsMagma_176
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma.setoid
d_setoid_200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> T_Setoid_44
d_setoid_200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 = T_IsMagma_176 -> T_Setoid_44
du_setoid_200 T_IsMagma_176
v5
du_setoid_200 ::
  T_IsMagma_176 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_200 :: T_IsMagma_176 -> T_Setoid_44
du_setoid_200 T_IsMagma_176
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_733
      (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma.∙-congˡ
d_'8729''45'cong'737'_202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8729''45'cong'737'_202 ::
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 :: T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 T_IsMagma_176
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 T_IsMagma_176
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Structures.IsMagma.∙-congʳ
d_'8729''45'cong'691'_206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_206 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_206 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8729''45'cong'691'_206 ::
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 :: T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 T_IsMagma_176
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 T_IsMagma_176
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0)) AgdaAny
v1)
-- Algebra.Structures.IsCommutativeMagma
d_IsCommutativeMagma_212 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMagma_212 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeMagma_212
  = C_IsCommutativeMagma'46'constructor_3749 T_IsMagma_176
                                             (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMagma.isMagma
d_isMagma_220 :: T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 :: T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 T_IsCommutativeMagma_212
v0
  = case T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0 of
      C_IsCommutativeMagma'46'constructor_3749 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsCommutativeMagma_212
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma.comm
d_comm_222 ::
  T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_222 :: T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_222 T_IsCommutativeMagma_212
v0
  = case T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0 of
      C_IsCommutativeMagma'46'constructor_3749 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMagma_212
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma._.isEquivalence
d_isEquivalence_226 ::
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_226 :: T_IsCommutativeMagma_212 -> T_IsEquivalence_26
d_isEquivalence_226 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.isPartialEquivalence
d_isPartialEquivalence_228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_228 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_228 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5
  = T_IsCommutativeMagma_212 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_228 T_IsCommutativeMagma_212
v5
du_isPartialEquivalence_228 ::
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_228 :: T_IsCommutativeMagma_212 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_228 T_IsCommutativeMagma_212
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsCommutativeMagma._.refl
d_refl_230 :: T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny
d_refl_230 :: T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny
d_refl_230 T_IsCommutativeMagma_212
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0)))
-- Algebra.Structures.IsCommutativeMagma._.reflexive
d_reflexive_232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_232 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_232 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5 = T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_232 T_IsCommutativeMagma_212
v5
du_reflexive_232 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_232 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_232 T_IsCommutativeMagma_212
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsCommutativeMagma._.setoid
d_setoid_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> T_Setoid_44
d_setoid_234 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5 = T_IsCommutativeMagma_212 -> T_Setoid_44
du_setoid_234 T_IsCommutativeMagma_212
v5
du_setoid_234 ::
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_234 :: T_IsCommutativeMagma_212 -> T_Setoid_44
du_setoid_234 T_IsCommutativeMagma_212
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.sym
d_sym_236 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 T_IsCommutativeMagma_212
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0)))
-- Algebra.Structures.IsCommutativeMagma._.trans
d_trans_238 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 T_IsCommutativeMagma_212
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0)))
-- Algebra.Structures.IsCommutativeMagma._.∙-cong
d_'8729''45'cong_240 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_240 :: T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_240 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.∙-congʳ
d_'8729''45'cong'691'_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_242 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5
  = T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_242 T_IsCommutativeMagma_212
v5
du_'8729''45'cong'691'_242 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_242 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_242 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.∙-congˡ
d_'8729''45'cong'737'_244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5
  = T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_244 T_IsCommutativeMagma_212
v5
du_'8729''45'cong'737'_244 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_244 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_244 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsIdempotentMagma
d_IsIdempotentMagma_248 :: p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentMagma_248 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsIdempotentMagma_248
  = C_IsIdempotentMagma'46'constructor_4535 T_IsMagma_176
                                            (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentMagma.isMagma
d_isMagma_256 :: T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 :: T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 T_IsIdempotentMagma_248
v0
  = case T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0 of
      C_IsIdempotentMagma'46'constructor_4535 T_IsMagma_176
v1 AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsIdempotentMagma_248
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMagma.idem
d_idem_258 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_idem_258 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_idem_258 T_IsIdempotentMagma_248
v0
  = case T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0 of
      C_IsIdempotentMagma'46'constructor_4535 T_IsMagma_176
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentMagma_248
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMagma._.isEquivalence
d_isEquivalence_262 ::
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_262 :: T_IsIdempotentMagma_248 -> T_IsEquivalence_26
d_isEquivalence_262 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.isPartialEquivalence
d_isPartialEquivalence_264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5
  = T_IsIdempotentMagma_248 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_IsIdempotentMagma_248
v5
du_isPartialEquivalence_264 ::
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_264 :: T_IsIdempotentMagma_248 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_IsIdempotentMagma_248
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsIdempotentMagma._.refl
d_refl_266 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_refl_266 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_refl_266 T_IsIdempotentMagma_248
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0)))
-- Algebra.Structures.IsIdempotentMagma._.reflexive
d_reflexive_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_268 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5 = T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_268 T_IsIdempotentMagma_248
v5
du_reflexive_268 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_268 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_268 T_IsIdempotentMagma_248
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsIdempotentMagma._.setoid
d_setoid_270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> T_Setoid_44
d_setoid_270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5 = T_IsIdempotentMagma_248 -> T_Setoid_44
du_setoid_270 T_IsIdempotentMagma_248
v5
du_setoid_270 ::
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_270 :: T_IsIdempotentMagma_248 -> T_Setoid_44
du_setoid_270 T_IsIdempotentMagma_248
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.sym
d_sym_272 ::
  T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_272 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_272 T_IsIdempotentMagma_248
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0)))
-- Algebra.Structures.IsIdempotentMagma._.trans
d_trans_274 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_274 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_274 T_IsIdempotentMagma_248
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0)))
-- Algebra.Structures.IsIdempotentMagma._.∙-cong
d_'8729''45'cong_276 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_276 :: T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_276 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.∙-congʳ
d_'8729''45'cong'691'_278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_278 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_278 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5
  = T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_278 T_IsIdempotentMagma_248
v5
du_'8729''45'cong'691'_278 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_278 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_278 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.∙-congˡ
d_'8729''45'cong'737'_280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_280 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5
  = T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_280 T_IsIdempotentMagma_248
v5
du_'8729''45'cong'737'_280 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_280 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_280 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsAlternativeMagma
d_IsAlternativeMagma_284 :: p -> p -> p -> p -> p -> T_Level_18
d_IsAlternativeMagma_284 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsAlternativeMagma_284
  = C_IsAlternativeMagma'46'constructor_5319 T_IsMagma_176
                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsAlternativeMagma.isMagma
d_isMagma_292 :: T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 :: T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 T_IsAlternativeMagma_284
v0
  = case T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0 of
      C_IsAlternativeMagma'46'constructor_5319 T_IsMagma_176
v1 T_Σ_14
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsAlternativeMagma_284
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAlternativeMagma.alter
d_alter_294 ::
  T_IsAlternativeMagma_284 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_alter_294 :: T_IsAlternativeMagma_284 -> T_Σ_14
d_alter_294 T_IsAlternativeMagma_284
v0
  = case T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0 of
      C_IsAlternativeMagma'46'constructor_5319 T_IsMagma_176
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsAlternativeMagma_284
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAlternativeMagma._.isEquivalence
d_isEquivalence_298 ::
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_298 :: T_IsAlternativeMagma_284 -> T_IsEquivalence_26
d_isEquivalence_298 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.isPartialEquivalence
d_isPartialEquivalence_300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_300 T_IsAlternativeMagma_284
v5
du_isPartialEquivalence_300 ::
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_300 :: T_IsAlternativeMagma_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_300 T_IsAlternativeMagma_284
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsAlternativeMagma._.refl
d_refl_302 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny
d_refl_302 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny
d_refl_302 T_IsAlternativeMagma_284
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0)))
-- Algebra.Structures.IsAlternativeMagma._.reflexive
d_reflexive_304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_304 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5 = T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_IsAlternativeMagma_284
v5
du_reflexive_304 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_304 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_IsAlternativeMagma_284
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsAlternativeMagma._.setoid
d_setoid_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> T_Setoid_44
d_setoid_306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5 = T_IsAlternativeMagma_284 -> T_Setoid_44
du_setoid_306 T_IsAlternativeMagma_284
v5
du_setoid_306 ::
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_306 :: T_IsAlternativeMagma_284 -> T_Setoid_44
du_setoid_306 T_IsAlternativeMagma_284
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.sym
d_sym_308 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 T_IsAlternativeMagma_284
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0)))
-- Algebra.Structures.IsAlternativeMagma._.trans
d_trans_310 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 T_IsAlternativeMagma_284
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0)))
-- Algebra.Structures.IsAlternativeMagma._.∙-cong
d_'8729''45'cong_312 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_312 :: T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_312 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.∙-congʳ
d_'8729''45'cong'691'_314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_IsAlternativeMagma_284
v5
du_'8729''45'cong'691'_314 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.∙-congˡ
d_'8729''45'cong'737'_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_IsAlternativeMagma_284
v5
du_'8729''45'cong'737'_316 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma.alternativeˡ
d_alternative'737'_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'737'_318 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_alternative'737'_318 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_318 T_IsAlternativeMagma_284
v5
du_alternative'737'_318 ::
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_318 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_318 T_IsAlternativeMagma_284
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 ((T_IsAlternativeMagma_284 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_Σ_14
d_alter_294 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma.alternativeʳ
d_alternative'691'_320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'691'_320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_alternative'691'_320 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_320 T_IsAlternativeMagma_284
v5
du_alternative'691'_320 ::
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_320 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_320 T_IsAlternativeMagma_284
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 ((T_IsAlternativeMagma_284 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_Σ_14
d_alter_294 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsFlexibleMagma
d_IsFlexibleMagma_324 :: p -> p -> p -> p -> p -> T_Level_18
d_IsFlexibleMagma_324 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsFlexibleMagma_324
  = C_IsFlexibleMagma'46'constructor_6681 T_IsMagma_176
                                          (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsFlexibleMagma.isMagma
d_isMagma_332 :: T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 :: T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 T_IsFlexibleMagma_324
v0
  = case T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0 of
      C_IsFlexibleMagma'46'constructor_6681 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsFlexibleMagma_324
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsFlexibleMagma.flex
d_flex_334 ::
  T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_334 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_334 T_IsFlexibleMagma_324
v0
  = case T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0 of
      C_IsFlexibleMagma'46'constructor_6681 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsFlexibleMagma_324
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsFlexibleMagma._.isEquivalence
d_isEquivalence_338 ::
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_338 :: T_IsFlexibleMagma_324 -> T_IsEquivalence_26
d_isEquivalence_338 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.isPartialEquivalence
d_isPartialEquivalence_340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5
  = T_IsFlexibleMagma_324 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_340 T_IsFlexibleMagma_324
v5
du_isPartialEquivalence_340 ::
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_340 :: T_IsFlexibleMagma_324 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_340 T_IsFlexibleMagma_324
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsFlexibleMagma._.refl
d_refl_342 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny
d_refl_342 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny
d_refl_342 T_IsFlexibleMagma_324
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0)))
-- Algebra.Structures.IsFlexibleMagma._.reflexive
d_reflexive_344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_344 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5 = T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsFlexibleMagma_324
v5
du_reflexive_344 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_344 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsFlexibleMagma_324
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsFlexibleMagma._.setoid
d_setoid_346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> T_Setoid_44
d_setoid_346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5 = T_IsFlexibleMagma_324 -> T_Setoid_44
du_setoid_346 T_IsFlexibleMagma_324
v5
du_setoid_346 ::
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_346 :: T_IsFlexibleMagma_324 -> T_Setoid_44
du_setoid_346 T_IsFlexibleMagma_324
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.sym
d_sym_348 ::
  T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_348 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_348 T_IsFlexibleMagma_324
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0)))
-- Algebra.Structures.IsFlexibleMagma._.trans
d_trans_350 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_350 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_350 T_IsFlexibleMagma_324
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0)))
-- Algebra.Structures.IsFlexibleMagma._.∙-cong
d_'8729''45'cong_352 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_352 :: T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_352 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.∙-congʳ
d_'8729''45'cong'691'_354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_354 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5
  = T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 T_IsFlexibleMagma_324
v5
du_'8729''45'cong'691'_354 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.∙-congˡ
d_'8729''45'cong'737'_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5
  = T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 T_IsFlexibleMagma_324
v5
du_'8729''45'cong'737'_356 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsMedialMagma
d_IsMedialMagma_360 :: p -> p -> p -> p -> p -> T_Level_18
d_IsMedialMagma_360 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsMedialMagma_360
  = C_IsMedialMagma'46'constructor_7467 T_IsMagma_176
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMedialMagma.isMagma
d_isMagma_368 :: T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 :: T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 T_IsMedialMagma_360
v0
  = case T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v0 of
      C_IsMedialMagma'46'constructor_7467 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsMedialMagma_360
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMedialMagma.medial
d_medial_370 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_370 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_370 T_IsMedialMagma_360
v0
  = case T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v0 of
      C_IsMedialMagma'46'constructor_7467 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMedialMagma_360
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMedialMagma._.isEquivalence
d_isEquivalence_374 ::
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_374 :: T_IsMedialMagma_360 -> T_IsEquivalence_26
d_isEquivalence_374 T_IsMedialMagma_360
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.isPartialEquivalence
d_isPartialEquivalence_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_376 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_376 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5
  = T_IsMedialMagma_360 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_IsMedialMagma_360
v5
du_isPartialEquivalence_376 ::
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_376 :: T_IsMedialMagma_360 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_IsMedialMagma_360
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsMedialMagma._.refl
d_refl_378 :: T_IsMedialMagma_360 -> AgdaAny -> AgdaAny
d_refl_378 :: T_IsMedialMagma_360 -> AgdaAny -> AgdaAny
d_refl_378 T_IsMedialMagma_360
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0)))
-- Algebra.Structures.IsMedialMagma._.reflexive
d_reflexive_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_380 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5 = T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_380 T_IsMedialMagma_360
v5
du_reflexive_380 ::
  T_IsMedialMagma_360 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_380 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_380 T_IsMedialMagma_360
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsMedialMagma._.setoid
d_setoid_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> T_Setoid_44
d_setoid_382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5 = T_IsMedialMagma_360 -> T_Setoid_44
du_setoid_382 T_IsMedialMagma_360
v5
du_setoid_382 ::
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_382 :: T_IsMedialMagma_360 -> T_Setoid_44
du_setoid_382 T_IsMedialMagma_360
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.sym
d_sym_384 ::
  T_IsMedialMagma_360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_384 :: T_IsMedialMagma_360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_384 T_IsMedialMagma_360
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0)))
-- Algebra.Structures.IsMedialMagma._.trans
d_trans_386 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_386 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_386 T_IsMedialMagma_360
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0)))
-- Algebra.Structures.IsMedialMagma._.∙-cong
d_'8729''45'cong_388 ::
  T_IsMedialMagma_360 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_388 :: T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_388 T_IsMedialMagma_360
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.∙-congʳ
d_'8729''45'cong'691'_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5
  = T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_390 T_IsMedialMagma_360
v5
du_'8729''45'cong'691'_390 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_390 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_390 T_IsMedialMagma_360
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.∙-congˡ
d_'8729''45'cong'737'_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_392 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_392 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5
  = T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_392 T_IsMedialMagma_360
v5
du_'8729''45'cong'737'_392 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_392 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_392 T_IsMedialMagma_360
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsSemimedialMagma
d_IsSemimedialMagma_396 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemimedialMagma_396 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemimedialMagma_396
  = C_IsSemimedialMagma'46'constructor_8257 T_IsMagma_176
                                            MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemimedialMagma.isMagma
d_isMagma_404 :: T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 :: T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 T_IsSemimedialMagma_396
v0
  = case T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0 of
      C_IsSemimedialMagma'46'constructor_8257 T_IsMagma_176
v1 T_Σ_14
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsSemimedialMagma_396
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemimedialMagma.semiMedial
d_semiMedial_406 ::
  T_IsSemimedialMagma_396 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_semiMedial_406 :: T_IsSemimedialMagma_396 -> T_Σ_14
d_semiMedial_406 T_IsSemimedialMagma_396
v0
  = case T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0 of
      C_IsSemimedialMagma'46'constructor_8257 T_IsMagma_176
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsSemimedialMagma_396
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemimedialMagma._.isEquivalence
d_isEquivalence_410 ::
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_410 :: T_IsSemimedialMagma_396 -> T_IsEquivalence_26
d_isEquivalence_410 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.isPartialEquivalence
d_isPartialEquivalence_412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_412 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_412 T_IsSemimedialMagma_396
v5
du_isPartialEquivalence_412 ::
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_412 :: T_IsSemimedialMagma_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_412 T_IsSemimedialMagma_396
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsSemimedialMagma._.refl
d_refl_414 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny
d_refl_414 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny
d_refl_414 T_IsSemimedialMagma_396
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0)))
-- Algebra.Structures.IsSemimedialMagma._.reflexive
d_reflexive_416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_416 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5 = T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_416 T_IsSemimedialMagma_396
v5
du_reflexive_416 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_416 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_416 T_IsSemimedialMagma_396
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSemimedialMagma._.setoid
d_setoid_418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> T_Setoid_44
d_setoid_418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5 = T_IsSemimedialMagma_396 -> T_Setoid_44
du_setoid_418 T_IsSemimedialMagma_396
v5
du_setoid_418 ::
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_418 :: T_IsSemimedialMagma_396 -> T_Setoid_44
du_setoid_418 T_IsSemimedialMagma_396
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.sym
d_sym_420 ::
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 T_IsSemimedialMagma_396
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0)))
-- Algebra.Structures.IsSemimedialMagma._.trans
d_trans_422 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 T_IsSemimedialMagma_396
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0)))
-- Algebra.Structures.IsSemimedialMagma._.∙-cong
d_'8729''45'cong_424 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_424 :: T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_424 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.∙-congʳ
d_'8729''45'cong'691'_426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_426 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_426 T_IsSemimedialMagma_396
v5
du_'8729''45'cong'691'_426 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_426 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_426 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.∙-congˡ
d_'8729''45'cong'737'_428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_428 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_428 T_IsSemimedialMagma_396
v5
du_'8729''45'cong'737'_428 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_428 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_428 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma.semimedialˡ
d_semimedial'737'_430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'737'_430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'737'_430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_430 T_IsSemimedialMagma_396
v5
du_semimedial'737'_430 ::
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_430 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_430 T_IsSemimedialMagma_396
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsSemimedialMagma_396 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_Σ_14
d_semiMedial_406 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma.semimedialʳ
d_semimedial'691'_432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'691'_432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'691'_432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_432 T_IsSemimedialMagma_396
v5
du_semimedial'691'_432 ::
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_432 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_432 T_IsSemimedialMagma_396
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsSemimedialMagma_396 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_Σ_14
d_semiMedial_406 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSelectiveMagma
d_IsSelectiveMagma_436 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSelectiveMagma_436 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSelectiveMagma_436
  = C_IsSelectiveMagma'46'constructor_9631 T_IsMagma_176
                                           (AgdaAny ->
                                            AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30)
-- Algebra.Structures.IsSelectiveMagma.isMagma
d_isMagma_444 :: T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 :: T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 T_IsSelectiveMagma_436
v0
  = case T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0 of
      C_IsSelectiveMagma'46'constructor_9631 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsSelectiveMagma_436
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma.sel
d_sel_446 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_446 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_446 T_IsSelectiveMagma_436
v0
  = case T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0 of
      C_IsSelectiveMagma'46'constructor_9631 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 -> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8846'__30
v2
      T_IsSelectiveMagma_436
_ -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma._.isEquivalence
d_isEquivalence_450 ::
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_450 :: T_IsSelectiveMagma_436 -> T_IsEquivalence_26
d_isEquivalence_450 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.isPartialEquivalence
d_isPartialEquivalence_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_452 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5
  = T_IsSelectiveMagma_436 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_452 T_IsSelectiveMagma_436
v5
du_isPartialEquivalence_452 ::
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_452 :: T_IsSelectiveMagma_436 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_452 T_IsSelectiveMagma_436
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsSelectiveMagma._.refl
d_refl_454 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny
d_refl_454 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny
d_refl_454 T_IsSelectiveMagma_436
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)))
-- Algebra.Structures.IsSelectiveMagma._.reflexive
d_reflexive_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_456 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_456 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5 = T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_456 T_IsSelectiveMagma_436
v5
du_reflexive_456 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_456 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_456 T_IsSelectiveMagma_436
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSelectiveMagma._.setoid
d_setoid_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> T_Setoid_44
d_setoid_458 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5 = T_IsSelectiveMagma_436 -> T_Setoid_44
du_setoid_458 T_IsSelectiveMagma_436
v5
du_setoid_458 ::
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_458 :: T_IsSelectiveMagma_436 -> T_Setoid_44
du_setoid_458 T_IsSelectiveMagma_436
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.sym
d_sym_460 ::
  T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_460 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_460 T_IsSelectiveMagma_436
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)))
-- Algebra.Structures.IsSelectiveMagma._.trans
d_trans_462 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_462 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_462 T_IsSelectiveMagma_436
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)))
-- Algebra.Structures.IsSelectiveMagma._.∙-cong
d_'8729''45'cong_464 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_464 :: T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_464 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.∙-congʳ
d_'8729''45'cong'691'_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_466 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_466 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5
  = T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_466 T_IsSelectiveMagma_436
v5
du_'8729''45'cong'691'_466 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_466 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_466 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.∙-congˡ
d_'8729''45'cong'737'_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_468 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_468 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5
  = T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_468 T_IsSelectiveMagma_436
v5
du_'8729''45'cong'737'_468 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_468 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_468 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSemigroup
d_IsSemigroup_472 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemigroup_472 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemigroup_472
  = C_IsSemigroup'46'constructor_10417 T_IsMagma_176
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSemigroup.isMagma
d_isMagma_480 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 T_IsSemigroup_472
v0
  = case T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v0 of
      C_IsSemigroup'46'constructor_10417 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsSemigroup_472
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup.assoc
d_assoc_482 ::
  T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 T_IsSemigroup_472
v0
  = case T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v0 of
      C_IsSemigroup'46'constructor_10417 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemigroup_472
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup._.isEquivalence
d_isEquivalence_486 ::
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_486 :: T_IsSemigroup_472 -> T_IsEquivalence_26
d_isEquivalence_486 T_IsSemigroup_472
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.isPartialEquivalence
d_isPartialEquivalence_488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_488 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_488 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5
  = T_IsSemigroup_472 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_488 T_IsSemigroup_472
v5
du_isPartialEquivalence_488 ::
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_488 :: T_IsSemigroup_472 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_488 T_IsSemigroup_472
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsSemigroup._.refl
d_refl_490 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny
d_refl_490 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny
d_refl_490 T_IsSemigroup_472
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)))
-- Algebra.Structures.IsSemigroup._.reflexive
d_reflexive_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_492 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_492 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5 = T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_492 T_IsSemigroup_472
v5
du_reflexive_492 ::
  T_IsSemigroup_472 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_492 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_492 T_IsSemigroup_472
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSemigroup._.setoid
d_setoid_494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_494 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> T_Setoid_44
d_setoid_494 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5 = T_IsSemigroup_472 -> T_Setoid_44
du_setoid_494 T_IsSemigroup_472
v5
du_setoid_494 ::
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_494 :: T_IsSemigroup_472 -> T_Setoid_44
du_setoid_494 T_IsSemigroup_472
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.sym
d_sym_496 ::
  T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_496 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_496 T_IsSemigroup_472
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)))
-- Algebra.Structures.IsSemigroup._.trans
d_trans_498 ::
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_498 :: T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_498 T_IsSemigroup_472
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)))
-- Algebra.Structures.IsSemigroup._.∙-cong
d_'8729''45'cong_500 ::
  T_IsSemigroup_472 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_500 :: T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_500 T_IsSemigroup_472
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.∙-congʳ
d_'8729''45'cong'691'_502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_502 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_502 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5
  = T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_502 T_IsSemigroup_472
v5
du_'8729''45'cong'691'_502 ::
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_502 :: T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_502 T_IsSemigroup_472
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.∙-congˡ
d_'8729''45'cong'737'_504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_504 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_504 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5
  = T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_504 T_IsSemigroup_472
v5
du_'8729''45'cong'737'_504 ::
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_504 :: T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_504 T_IsSemigroup_472
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsBand
d_IsBand_508 :: p -> p -> p -> p -> p -> T_Level_18
d_IsBand_508 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsBand_508
  = C_IsBand'46'constructor_11205 T_IsSemigroup_472
                                  (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsBand.isSemigroup
d_isSemigroup_516 :: T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 :: T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 T_IsBand_508
v0
  = case T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0 of
      C_IsBand'46'constructor_11205 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1
      T_IsBand_508
_ -> T_IsSemigroup_472
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand.idem
d_idem_518 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_518 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_518 T_IsBand_508
v0
  = case T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0 of
      C_IsBand'46'constructor_11205 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBand_508
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand._.assoc
d_assoc_522 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_522 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_522 T_IsBand_508
v0 = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))
-- Algebra.Structures.IsBand._.isEquivalence
d_isEquivalence_524 ::
  T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_524 :: T_IsBand_508 -> T_IsEquivalence_26
d_isEquivalence_524 T_IsBand_508
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0)))
-- Algebra.Structures.IsBand._.isMagma
d_isMagma_526 :: T_IsBand_508 -> T_IsMagma_176
d_isMagma_526 :: T_IsBand_508 -> T_IsMagma_176
d_isMagma_526 T_IsBand_508
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))
-- Algebra.Structures.IsBand._.isPartialEquivalence
d_isPartialEquivalence_528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_528 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_528 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_528 T_IsBand_508
v5
du_isPartialEquivalence_528 ::
  T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_528 :: T_IsBand_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_528 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsBand._.refl
d_refl_530 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_refl_530 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_refl_530 T_IsBand_508
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))))
-- Algebra.Structures.IsBand._.reflexive
d_reflexive_532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_532 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_532 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = T_IsBand_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_532 T_IsBand_508
v5
du_reflexive_532 ::
  T_IsBand_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_532 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_532 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsBand._.setoid
d_setoid_534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_534 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_Setoid_44
d_setoid_534 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = T_IsBand_508 -> T_Setoid_44
du_setoid_534 T_IsBand_508
v5
du_setoid_534 ::
  T_IsBand_508 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_534 :: T_IsBand_508 -> T_Setoid_44
du_setoid_534 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsBand._.sym
d_sym_536 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_536 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_536 T_IsBand_508
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))))
-- Algebra.Structures.IsBand._.trans
d_trans_538 ::
  T_IsBand_508 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_538 :: T_IsBand_508
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_538 T_IsBand_508
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))))
-- Algebra.Structures.IsBand._.∙-cong
d_'8729''45'cong_540 ::
  T_IsBand_508 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_540 :: T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_540 T_IsBand_508
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0)))
-- Algebra.Structures.IsBand._.∙-congʳ
d_'8729''45'cong'691'_542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_542 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_542 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 T_IsBand_508
v5
du_'8729''45'cong'691'_542 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsBand._.∙-congˡ
d_'8729''45'cong'737'_544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_544 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_544 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 T_IsBand_508
v5
du_'8729''45'cong'737'_544 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup
d_IsCommutativeSemigroup_548 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemigroup_548 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeSemigroup_548
  = C_IsCommutativeSemigroup'46'constructor_12093 T_IsSemigroup_472
                                                  (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_556 ::
  T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 :: T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 T_IsCommutativeSemigroup_548
v0
  = case T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0 of
      C_IsCommutativeSemigroup'46'constructor_12093 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1
      T_IsCommutativeSemigroup_548
_ -> T_IsSemigroup_472
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup.comm
d_comm_558 ::
  T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_558 :: T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_558 T_IsCommutativeSemigroup_548
v0
  = case T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0 of
      C_IsCommutativeSemigroup'46'constructor_12093 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemigroup_548
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup._.assoc
d_assoc_562 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_562 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_562 T_IsCommutativeSemigroup_548
v0 = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isEquivalence
d_isEquivalence_564 ::
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_564 :: T_IsCommutativeSemigroup_548 -> T_IsEquivalence_26
d_isEquivalence_564 T_IsCommutativeSemigroup_548
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.isMagma
d_isMagma_566 :: T_IsCommutativeSemigroup_548 -> T_IsMagma_176
d_isMagma_566 :: T_IsCommutativeSemigroup_548 -> T_IsMagma_176
d_isMagma_566 T_IsCommutativeSemigroup_548
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isPartialEquivalence
d_isPartialEquivalence_568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_568 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_568 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_568 T_IsCommutativeSemigroup_548
v5
du_isPartialEquivalence_568 ::
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_568 :: T_IsCommutativeSemigroup_548 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_568 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsCommutativeSemigroup._.refl
d_refl_570 :: T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny
d_refl_570 :: T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny
d_refl_570 T_IsCommutativeSemigroup_548
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.reflexive
d_reflexive_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_572 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5 = T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_572 T_IsCommutativeSemigroup_548
v5
du_reflexive_572 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_572 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_572 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsCommutativeSemigroup._.setoid
d_setoid_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> T_Setoid_44
d_setoid_574 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5 = T_IsCommutativeSemigroup_548 -> T_Setoid_44
du_setoid_574 T_IsCommutativeSemigroup_548
v5
du_setoid_574 ::
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_574 :: T_IsCommutativeSemigroup_548 -> T_Setoid_44
du_setoid_574 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup._.sym
d_sym_576 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_576 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_576 T_IsCommutativeSemigroup_548
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.trans
d_trans_578 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_578 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_578 T_IsCommutativeSemigroup_548
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-cong
d_'8729''45'cong_580 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_580 :: T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_580 T_IsCommutativeSemigroup_548
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congʳ
d_'8729''45'cong'691'_582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_582 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_582 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_582 T_IsCommutativeSemigroup_548
v5
du_'8729''45'cong'691'_582 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_582 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_582 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congˡ
d_'8729''45'cong'737'_584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_584 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_584 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_584 T_IsCommutativeSemigroup_548
v5
du_'8729''45'cong'737'_584 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_584 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_584 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup.isCommutativeMagma
d_isCommutativeMagma_586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_586 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_586 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586 T_IsCommutativeSemigroup_548
v5
du_isCommutativeMagma_586 ::
  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586 :: T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586 T_IsCommutativeSemigroup_548
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_212
C_IsCommutativeMagma'46'constructor_3749
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)))
      ((T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_558 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))
-- Algebra.Structures.IsCommutativeBand
d_IsCommutativeBand_590 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeBand_590 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeBand_590
  = C_IsCommutativeBand'46'constructor_13109 T_IsBand_508
                                             (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeBand.isBand
d_isBand_598 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 T_IsCommutativeBand_590
v0
  = case T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0 of
      C_IsCommutativeBand'46'constructor_13109 T_IsBand_508
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1
      T_IsCommutativeBand_590
_ -> T_IsBand_508
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeBand.comm
d_comm_600 ::
  T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_600 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_600 T_IsCommutativeBand_590
v0
  = case T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0 of
      C_IsCommutativeBand'46'constructor_13109 T_IsBand_508
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeBand_590
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeBand._.assoc
d_assoc_604 ::
  T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_604 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_604 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Structures.IsCommutativeBand._.idem
d_idem_606 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_idem_606 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_idem_606 T_IsCommutativeBand_590
v0 = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_518 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsCommutativeBand._.isEquivalence
d_isEquivalence_608 ::
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_608 :: T_IsCommutativeBand_590 -> T_IsEquivalence_26
d_isEquivalence_608 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Structures.IsCommutativeBand._.isMagma
d_isMagma_610 :: T_IsCommutativeBand_590 -> T_IsMagma_176
d_isMagma_610 :: T_IsCommutativeBand_590 -> T_IsMagma_176
d_isMagma_610 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Structures.IsCommutativeBand._.isPartialEquivalence
d_isPartialEquivalence_612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_612 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_612 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_612 T_IsCommutativeBand_590
v5
du_isPartialEquivalence_612 ::
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_612 :: T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_612 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsCommutativeBand._.isSemigroup
d_isSemigroup_614 :: T_IsCommutativeBand_590 -> T_IsSemigroup_472
d_isSemigroup_614 :: T_IsCommutativeBand_590 -> T_IsSemigroup_472
d_isSemigroup_614 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsCommutativeBand._.refl
d_refl_616 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_refl_616 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_refl_616 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Structures.IsCommutativeBand._.reflexive
d_reflexive_618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_618 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_618 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_618 T_IsCommutativeBand_590
v5
du_reflexive_618 ::
  T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_618 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_618 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsCommutativeBand._.setoid
d_setoid_620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_620 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Setoid_44
d_setoid_620 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_620 T_IsCommutativeBand_590
v5
du_setoid_620 ::
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_620 :: T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_620 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeBand._.sym
d_sym_622 ::
  T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_622 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_622 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Structures.IsCommutativeBand._.trans
d_trans_624 ::
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_624 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_624 T_IsCommutativeBand_590
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Structures.IsCommutativeBand._.∙-cong
d_'8729''45'cong_626 ::
  T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_626 :: T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_626 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Structures.IsCommutativeBand._.∙-congʳ
d_'8729''45'cong'691'_628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_628 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_628 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_628 T_IsCommutativeBand_590
v5
du_'8729''45'cong'691'_628 ::
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_628 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_628 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeBand._.∙-congˡ
d_'8729''45'cong'737'_630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_630 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_630 T_IsCommutativeBand_590
v5
du_'8729''45'cong'737'_630 ::
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_630 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_630 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeBand.isCommutativeSemigroup
d_isCommutativeSemigroup_632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 T_IsCommutativeBand_590
v5
du_isCommutativeSemigroup_632 ::
  T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 :: T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548
C_IsCommutativeSemigroup'46'constructor_12093
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
      ((T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsCommutativeBand._.isCommutativeMagma
d_isCommutativeMagma_636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_636 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_636 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_636 T_IsCommutativeBand_590
v5
du_isCommutativeMagma_636 ::
  T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_636 :: T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_636 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
      ((T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsUnitalMagma
d_IsUnitalMagma_642 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsUnitalMagma_642 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsUnitalMagma_642
  = C_IsUnitalMagma'46'constructor_14317 T_IsMagma_176
                                         MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsUnitalMagma.isMagma
d_isMagma_652 :: T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 :: T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 T_IsUnitalMagma_642
v0
  = case T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v0 of
      C_IsUnitalMagma'46'constructor_14317 T_IsMagma_176
v1 T_Σ_14
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsUnitalMagma_642
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsUnitalMagma.identity
d_identity_654 ::
  T_IsUnitalMagma_642 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_654 :: T_IsUnitalMagma_642 -> T_Σ_14
d_identity_654 T_IsUnitalMagma_642
v0
  = case T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v0 of
      C_IsUnitalMagma'46'constructor_14317 T_IsMagma_176
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsUnitalMagma_642
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsUnitalMagma._.isEquivalence
d_isEquivalence_658 ::
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_658 :: T_IsUnitalMagma_642 -> T_IsEquivalence_26
d_isEquivalence_658 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_660 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_660 T_IsUnitalMagma_642
v6
du_isPartialEquivalence_660 ::
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_660 :: T_IsUnitalMagma_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_660 T_IsUnitalMagma_642
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsUnitalMagma._.refl
d_refl_662 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_refl_662 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_refl_662 T_IsUnitalMagma_642
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0)))
-- Algebra.Structures.IsUnitalMagma._.reflexive
d_reflexive_664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_664 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_664 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_642
v6 = T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_664 T_IsUnitalMagma_642
v6
du_reflexive_664 ::
  T_IsUnitalMagma_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_664 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_664 T_IsUnitalMagma_642
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsUnitalMagma._.setoid
d_setoid_666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_666 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> T_Setoid_44
d_setoid_666 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_642
v6 = T_IsUnitalMagma_642 -> T_Setoid_44
du_setoid_666 T_IsUnitalMagma_642
v6
du_setoid_666 ::
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_666 :: T_IsUnitalMagma_642 -> T_Setoid_44
du_setoid_666 T_IsUnitalMagma_642
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.sym
d_sym_668 ::
  T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_668 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_668 T_IsUnitalMagma_642
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0)))
-- Algebra.Structures.IsUnitalMagma._.trans
d_trans_670 ::
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_670 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_670 T_IsUnitalMagma_642
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0)))
-- Algebra.Structures.IsUnitalMagma._.∙-cong
d_'8729''45'cong_672 ::
  T_IsUnitalMagma_642 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_672 :: T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_672 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_674 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_674 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_674 T_IsUnitalMagma_642
v6
du_'8729''45'cong'691'_674 ::
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_674 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_674 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_676 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_676 T_IsUnitalMagma_642
v6
du_'8729''45'cong'737'_676 ::
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_676 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_676 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma.identityˡ
d_identity'737'_678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_identity'737'_678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
d_identity'737'_678 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'737'_678 T_IsUnitalMagma_642
v6
du_identity'737'_678 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'737'_678 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'737'_678 T_IsUnitalMagma_642
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsUnitalMagma_642 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_Σ_14
d_identity_654 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma.identityʳ
d_identity'691'_680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_identity'691'_680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
d_identity'691'_680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'691'_680 T_IsUnitalMagma_642
v6
du_identity'691'_680 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'691'_680 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'691'_680 T_IsUnitalMagma_642
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsUnitalMagma_642 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_Σ_14
d_identity_654 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsMonoid
d_IsMonoid_686 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoid_686 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsMonoid_686
  = C_IsMonoid'46'constructor_15873 T_IsSemigroup_472
                                    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsMonoid.isSemigroup
d_isSemigroup_696 :: T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 :: T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 T_IsMonoid_686
v0
  = case T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0 of
      C_IsMonoid'46'constructor_15873 T_IsSemigroup_472
v1 T_Σ_14
v2 -> T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1
      T_IsMonoid_686
_ -> T_IsSemigroup_472
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid.identity
d_identity_698 ::
  T_IsMonoid_686 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_698 :: T_IsMonoid_686 -> T_Σ_14
d_identity_698 T_IsMonoid_686
v0
  = case T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0 of
      C_IsMonoid'46'constructor_15873 T_IsSemigroup_472
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsMonoid_686
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid._.assoc
d_assoc_702 ::
  T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_702 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_702 T_IsMonoid_686
v0 = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid._.isEquivalence
d_isEquivalence_704 ::
  T_IsMonoid_686 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_704 :: T_IsMonoid_686 -> T_IsEquivalence_26
d_isEquivalence_704 T_IsMonoid_686
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)))
-- Algebra.Structures.IsMonoid._.isMagma
d_isMagma_706 :: T_IsMonoid_686 -> T_IsMagma_176
d_isMagma_706 :: T_IsMonoid_686 -> T_IsMagma_176
d_isMagma_706 T_IsMonoid_686
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid._.isPartialEquivalence
d_isPartialEquivalence_708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6
  = T_IsMonoid_686 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_708 T_IsMonoid_686
v6
du_isPartialEquivalence_708 ::
  T_IsMonoid_686 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_708 :: T_IsMonoid_686 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_708 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsMonoid._.refl
d_refl_710 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_refl_710 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_refl_710 T_IsMonoid_686
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))))
-- Algebra.Structures.IsMonoid._.reflexive
d_reflexive_712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_712 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6 = T_IsMonoid_686 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_712 T_IsMonoid_686
v6
du_reflexive_712 ::
  T_IsMonoid_686 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_712 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_712 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsMonoid._.setoid
d_setoid_714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_714 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_Setoid_44
d_setoid_714 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6 = T_IsMonoid_686 -> T_Setoid_44
du_setoid_714 T_IsMonoid_686
v6
du_setoid_714 ::
  T_IsMonoid_686 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_714 :: T_IsMonoid_686 -> T_Setoid_44
du_setoid_714 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsMonoid._.sym
d_sym_716 ::
  T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_716 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_716 T_IsMonoid_686
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))))
-- Algebra.Structures.IsMonoid._.trans
d_trans_718 ::
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_718 :: T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_718 T_IsMonoid_686
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))))
-- Algebra.Structures.IsMonoid._.∙-cong
d_'8729''45'cong_720 ::
  T_IsMonoid_686 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_720 :: T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_720 T_IsMonoid_686
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)))
-- Algebra.Structures.IsMonoid._.∙-congʳ
d_'8729''45'cong'691'_722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_722 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6
  = T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_722 T_IsMonoid_686
v6
du_'8729''45'cong'691'_722 ::
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_722 :: T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_722 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsMonoid._.∙-congˡ
d_'8729''45'cong'737'_724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6
  = T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_724 T_IsMonoid_686
v6
du_'8729''45'cong'737'_724 ::
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_724 :: T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_724 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsMonoid.identityˡ
d_identity'737'_726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_identity'737'_726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
d_identity'737'_726 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6
  = T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 T_IsMonoid_686
v6
du_identity'737'_726 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 T_IsMonoid_686
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid.identityʳ
d_identity'691'_728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_identity'691'_728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
d_identity'691'_728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6
  = T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 T_IsMonoid_686
v6
du_identity'691'_728 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 T_IsMonoid_686
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid.isUnitalMagma
d_isUnitalMagma_730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_686 -> T_IsUnitalMagma_642
d_isUnitalMagma_730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_IsUnitalMagma_642
d_isUnitalMagma_730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_686
v6
  = T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 T_IsMonoid_686
v6
du_isUnitalMagma_730 :: T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 :: T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 T_IsMonoid_686
v0
  = (T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642)
-> AgdaAny -> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642
C_IsUnitalMagma'46'constructor_14317
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsCommutativeMonoid
d_IsCommutativeMonoid_736 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMonoid_736 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsCommutativeMonoid_736
  = C_IsCommutativeMonoid'46'constructor_17695 T_IsMonoid_686
                                               (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMonoid.isMonoid
d_isMonoid_746 :: T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 :: T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 T_IsCommutativeMonoid_736
v0
  = case T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0 of
      C_IsCommutativeMonoid'46'constructor_17695 T_IsMonoid_686
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsCommutativeMonoid_736
_ -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid.comm
d_comm_748 ::
  T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 T_IsCommutativeMonoid_736
v0
  = case T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0 of
      C_IsCommutativeMonoid'46'constructor_17695 T_IsMonoid_686
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMonoid_736
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid._.assoc
d_assoc_752 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_752 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_752 T_IsCommutativeMonoid_736
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.identity
d_identity_754 ::
  T_IsCommutativeMonoid_736 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_754 :: T_IsCommutativeMonoid_736 -> T_Σ_14
d_identity_754 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityʳ
d_identity'691'_756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_identity'691'_756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
d_identity'691'_756 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'691'_756 T_IsCommutativeMonoid_736
v6
du_identity'691'_756 ::
  T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'691'_756 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'691'_756 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityˡ
d_identity'737'_758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_identity'737'_758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
d_identity'737'_758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'737'_758 T_IsCommutativeMonoid_736
v6
du_identity'737'_758 ::
  T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'737'_758 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'737'_758 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isEquivalence
d_isEquivalence_760 ::
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_760 :: T_IsCommutativeMonoid_736 -> T_IsEquivalence_26
d_isEquivalence_760 T_IsCommutativeMonoid_736
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.isMagma
d_isMagma_762 :: T_IsCommutativeMonoid_736 -> T_IsMagma_176
d_isMagma_762 :: T_IsCommutativeMonoid_736 -> T_IsMagma_176
d_isMagma_762 T_IsCommutativeMonoid_736
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_764 T_IsCommutativeMonoid_736
v6
du_isPartialEquivalence_764 ::
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_764 :: T_IsCommutativeMonoid_736 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_764 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsCommutativeMonoid._.isSemigroup
d_isSemigroup_766 :: T_IsCommutativeMonoid_736 -> T_IsSemigroup_472
d_isSemigroup_766 :: T_IsCommutativeMonoid_736 -> T_IsSemigroup_472
d_isSemigroup_766 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
d_isUnitalMagma_768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsUnitalMagma_642
d_isUnitalMagma_768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
du_isUnitalMagma_768 T_IsCommutativeMonoid_736
v6
du_isUnitalMagma_768 ::
  T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
du_isUnitalMagma_768 :: T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
du_isUnitalMagma_768 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.refl
d_refl_770 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_refl_770 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_refl_770 T_IsCommutativeMonoid_736
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.reflexive
d_reflexive_772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6 = T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_772 T_IsCommutativeMonoid_736
v6
du_reflexive_772 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_772 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_772 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsCommutativeMonoid._.setoid
d_setoid_774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_Setoid_44
d_setoid_774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6 = T_IsCommutativeMonoid_736 -> T_Setoid_44
du_setoid_774 T_IsCommutativeMonoid_736
v6
du_setoid_774 ::
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_774 :: T_IsCommutativeMonoid_736 -> T_Setoid_44
du_setoid_774 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeMonoid._.sym
d_sym_776 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_776 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_776 T_IsCommutativeMonoid_736
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.trans
d_trans_778 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_778 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_778 T_IsCommutativeMonoid_736
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-cong
d_'8729''45'cong_780 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_780 :: T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_780 T_IsCommutativeMonoid_736
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_782 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_782 T_IsCommutativeMonoid_736
v6
du_'8729''45'cong'691'_782 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_782 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_782 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_784 T_IsCommutativeMonoid_736
v6
du_'8729''45'cong'737'_784 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_784 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_784 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_786 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 T_IsCommutativeMonoid_736
v6
du_isCommutativeSemigroup_786 ::
  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 :: T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 T_IsCommutativeMonoid_736
v0
  = (T_IsSemigroup_472
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548
C_IsCommutativeSemigroup'46'constructor_12093
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))
      ((T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_790 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_790 T_IsCommutativeMonoid_736
v6
du_isCommutativeMagma_790 ::
  T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_790 :: T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_790 T_IsCommutativeMonoid_736
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsIdempotentMonoid
d_IsIdempotentMonoid_796 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentMonoid_796 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsIdempotentMonoid_796
  = C_IsIdempotentMonoid'46'constructor_19237 T_IsMonoid_686
                                              (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentMonoid.isMonoid
d_isMonoid_806 :: T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 :: T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 T_IsIdempotentMonoid_796
v0
  = case T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0 of
      C_IsIdempotentMonoid'46'constructor_19237 T_IsMonoid_686
v1 AgdaAny -> AgdaAny
v2 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsIdempotentMonoid_796
_ -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMonoid.idem
d_idem_808 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_idem_808 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_idem_808 T_IsIdempotentMonoid_796
v0
  = case T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0 of
      C_IsIdempotentMonoid'46'constructor_19237 T_IsMonoid_686
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentMonoid_796
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMonoid._.assoc
d_assoc_812 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_812 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_812 T_IsIdempotentMonoid_796
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))
-- Algebra.Structures.IsIdempotentMonoid._.identity
d_identity_814 ::
  T_IsIdempotentMonoid_796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_814 :: T_IsIdempotentMonoid_796 -> T_Σ_14
d_identity_814 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.identityʳ
d_identity'691'_816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_identity'691'_816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
d_identity'691'_816 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'691'_816 T_IsIdempotentMonoid_796
v6
du_identity'691'_816 ::
  T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'691'_816 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'691'_816 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.identityˡ
d_identity'737'_818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_identity'737'_818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
d_identity'737'_818 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'737'_818 T_IsIdempotentMonoid_796
v6
du_identity'737'_818 ::
  T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'737'_818 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'737'_818 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.isEquivalence
d_isEquivalence_820 ::
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_820 :: T_IsIdempotentMonoid_796 -> T_IsEquivalence_26
d_isEquivalence_820 T_IsIdempotentMonoid_796
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))))
-- Algebra.Structures.IsIdempotentMonoid._.isMagma
d_isMagma_822 :: T_IsIdempotentMonoid_796 -> T_IsMagma_176
d_isMagma_822 :: T_IsIdempotentMonoid_796 -> T_IsMagma_176
d_isMagma_822 T_IsIdempotentMonoid_796
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))
-- Algebra.Structures.IsIdempotentMonoid._.isPartialEquivalence
d_isPartialEquivalence_824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_824 T_IsIdempotentMonoid_796
v6
du_isPartialEquivalence_824 ::
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_824 :: T_IsIdempotentMonoid_796 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_824 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsIdempotentMonoid._.isSemigroup
d_isSemigroup_826 :: T_IsIdempotentMonoid_796 -> T_IsSemigroup_472
d_isSemigroup_826 :: T_IsIdempotentMonoid_796 -> T_IsSemigroup_472
d_isSemigroup_826 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.isUnitalMagma
d_isUnitalMagma_828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
d_isUnitalMagma_828 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_IsUnitalMagma_642
d_isUnitalMagma_828 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
du_isUnitalMagma_828 T_IsIdempotentMonoid_796
v6
du_isUnitalMagma_828 ::
  T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
du_isUnitalMagma_828 :: T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
du_isUnitalMagma_828 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.refl
d_refl_830 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_refl_830 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_refl_830 T_IsIdempotentMonoid_796
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.reflexive
d_reflexive_832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6 = T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_832 T_IsIdempotentMonoid_796
v6
du_reflexive_832 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_832 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_832 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsIdempotentMonoid._.setoid
d_setoid_834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_Setoid_44
d_setoid_834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6 = T_IsIdempotentMonoid_796 -> T_Setoid_44
du_setoid_834 T_IsIdempotentMonoid_796
v6
du_setoid_834 ::
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_834 :: T_IsIdempotentMonoid_796 -> T_Setoid_44
du_setoid_834 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsIdempotentMonoid._.sym
d_sym_836 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 T_IsIdempotentMonoid_796
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.trans
d_trans_838 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 T_IsIdempotentMonoid_796
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-cong
d_'8729''45'cong_840 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_840 :: T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_840 T_IsIdempotentMonoid_796
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-congʳ
d_'8729''45'cong'691'_842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_842 T_IsIdempotentMonoid_796
v6
du_'8729''45'cong'691'_842 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_842 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_842 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-congˡ
d_'8729''45'cong'737'_844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_844 T_IsIdempotentMonoid_796
v6
du_'8729''45'cong'737'_844 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_844 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_844 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsIdempotentMonoid.isBand
d_isBand_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> T_IsBand_508
d_isBand_846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_IsBand_508
d_isBand_846 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentMonoid_796
v6 = T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 T_IsIdempotentMonoid_796
v6
du_isBand_846 :: T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 :: T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 T_IsIdempotentMonoid_796
v0
  = (T_IsSemigroup_472 -> (AgdaAny -> AgdaAny) -> T_IsBand_508)
-> AgdaAny -> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsSemigroup_472 -> (AgdaAny -> AgdaAny) -> T_IsBand_508
C_IsBand'46'constructor_11205
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))
      ((T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_idem_808 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_852 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentCommutativeMonoid_852 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsIdempotentCommutativeMonoid_852
  = C_IsIdempotentCommutativeMonoid'46'constructor_20685 T_IsCommutativeMonoid_736
                                                         (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_862 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 T_IsIdempotentCommutativeMonoid_852
v0
  = case T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0 of
      C_IsIdempotentCommutativeMonoid'46'constructor_20685 T_IsCommutativeMonoid_736
v1 AgdaAny -> AgdaAny
v2
        -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1
      T_IsIdempotentCommutativeMonoid_852
_ -> T_IsCommutativeMonoid_736
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid.idem
d_idem_864 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_864 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_864 T_IsIdempotentCommutativeMonoid_852
v0
  = case T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0 of
      C_IsIdempotentCommutativeMonoid'46'constructor_20685 T_IsCommutativeMonoid_736
v1 AgdaAny -> AgdaAny
v2
        -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentCommutativeMonoid_852
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.assoc
d_assoc_868 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_868 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_868 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.comm
d_comm_870 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_870 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_870 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identity
d_identity_872 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_872 :: T_IsIdempotentCommutativeMonoid_852 -> T_Σ_14
d_identity_872 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityʳ
d_identity'691'_874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_identity'691'_874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'691'_874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_874 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'691'_874 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_874 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_874 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityˡ
d_identity'737'_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_identity'737'_876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'737'_876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_876 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'737'_876 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_876 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_876 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_878 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_878 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeMagma_878 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_878 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_878 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_880 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_880 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeSemigroup_880 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_880 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_880 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isEquivalence
d_isEquivalence_882 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_882 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsEquivalence_26
d_isEquivalence_882 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMagma
d_isMagma_884 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
d_isMagma_884 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
d_isMagma_884 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMonoid
d_isMonoid_886 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsMonoid_686
d_isMonoid_886 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMonoid_686
d_isMonoid_886 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_888 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_888 T_IsIdempotentCommutativeMonoid_852
v6
du_isPartialEquivalence_888 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_888 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_888 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isSemigroup
d_isSemigroup_890 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
d_isSemigroup_890 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
d_isSemigroup_890 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
d_isUnitalMagma_892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsUnitalMagma_642
d_isUnitalMagma_892 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_892 T_IsIdempotentCommutativeMonoid_852
v6
du_isUnitalMagma_892 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_892 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_892 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.refl
d_refl_894 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_refl_894 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_refl_894 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.reflexive
d_reflexive_896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_896 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_896 T_IsIdempotentCommutativeMonoid_852
v6
du_reflexive_896 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_896 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_896 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.setoid
d_setoid_898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_Setoid_44
d_setoid_898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_898 T_IsIdempotentCommutativeMonoid_852
v6
du_setoid_898 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_898 :: T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_898 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.sym
d_sym_900 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_900 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_900 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.trans
d_trans_902 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_902 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_902 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-cong
d_'8729''45'cong_904 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_904 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_904 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_906 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'691'_906 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'737'_908 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isIdempotentMonoid
d_isIdempotentMonoid_910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_910 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 T_IsIdempotentCommutativeMonoid_852
v6
du_isIdempotentMonoid_910 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686
 -> (AgdaAny -> AgdaAny) -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      T_IsMonoid_686 -> (AgdaAny -> AgdaAny) -> T_IsIdempotentMonoid_796
C_IsIdempotentMonoid'46'constructor_19237
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
      ((T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_864 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isBand
d_isBand_914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
d_isBand_914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsBand_508
d_isBand_914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_914 T_IsIdempotentCommutativeMonoid_852
v6
du_isBand_914 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_914 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_914 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentMonoid_796 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isCommutativeBand
d_isCommutativeBand_916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
d_isCommutativeBand_916 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
d_isCommutativeBand_916 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeBand_916 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsBand_508
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsBand_508
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeBand_590
C_IsCommutativeBand'46'constructor_13109
      ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
      ((T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Structures.IsInvertibleMagma
d_IsInvertibleMagma_924 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInvertibleMagma_924 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsInvertibleMagma_924
  = C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsInvertibleMagma.isMagma
d_isMagma_938 :: T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 :: T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 T_IsInvertibleMagma_924
v0
  = case T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0 of
      C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsInvertibleMagma_924
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma.inverse
d_inverse_940 ::
  T_IsInvertibleMagma_924 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_940 :: T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 T_IsInvertibleMagma_924
v0
  = case T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0 of
      C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsInvertibleMagma_924
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma.⁻¹-cong
d_'8315''185''45'cong_942 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_942 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_942 T_IsInvertibleMagma_924
v0
  = case T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0 of
      C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsInvertibleMagma_924
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma._.isEquivalence
d_isEquivalence_946 ::
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_946 :: T_IsInvertibleMagma_924 -> T_IsEquivalence_26
d_isEquivalence_946 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.isPartialEquivalence
d_isPartialEquivalence_948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_948 T_IsInvertibleMagma_924
v7
du_isPartialEquivalence_948 ::
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_948 :: T_IsInvertibleMagma_924 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_948 T_IsInvertibleMagma_924
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsInvertibleMagma._.refl
d_refl_950 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_refl_950 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_refl_950 T_IsInvertibleMagma_924
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0)))
-- Algebra.Structures.IsInvertibleMagma._.reflexive
d_reflexive_952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_952 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_952 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_952 T_IsInvertibleMagma_924
v7
du_reflexive_952 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_952 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_952 T_IsInvertibleMagma_924
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsInvertibleMagma._.setoid
d_setoid_954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> T_Setoid_44
d_setoid_954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_924
v7 = T_IsInvertibleMagma_924 -> T_Setoid_44
du_setoid_954 T_IsInvertibleMagma_924
v7
du_setoid_954 ::
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_954 :: T_IsInvertibleMagma_924 -> T_Setoid_44
du_setoid_954 T_IsInvertibleMagma_924
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.sym
d_sym_956 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_956 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_956 T_IsInvertibleMagma_924
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0)))
-- Algebra.Structures.IsInvertibleMagma._.trans
d_trans_958 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_958 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_958 T_IsInvertibleMagma_924
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0)))
-- Algebra.Structures.IsInvertibleMagma._.∙-cong
d_'8729''45'cong_960 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_960 :: T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_960 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.∙-congʳ
d_'8729''45'cong'691'_962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_962 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_962 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_962 T_IsInvertibleMagma_924
v7
du_'8729''45'cong'691'_962 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_962 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_962 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.∙-congˡ
d_'8729''45'cong'737'_964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_964 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_964 T_IsInvertibleMagma_924
v7
du_'8729''45'cong'737'_964 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_964 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_964 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma.inverseˡ
d_inverse'737'_966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_inverse'737'_966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
d_inverse'737'_966 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 T_IsInvertibleMagma_924
v7
du_inverse'737'_966 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 T_IsInvertibleMagma_924
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma.inverseʳ
d_inverse'691'_968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_inverse'691'_968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
d_inverse'691'_968 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 T_IsInvertibleMagma_924
v7
du_inverse'691'_968 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 T_IsInvertibleMagma_924
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma
d_IsInvertibleUnitalMagma_976 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInvertibleUnitalMagma_976 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsInvertibleUnitalMagma_976
  = C_IsInvertibleUnitalMagma'46'constructor_24571 T_IsInvertibleMagma_924
                                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsInvertibleUnitalMagma.isInvertibleMagma
d_isInvertibleMagma_988 ::
  T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 :: T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 T_IsInvertibleUnitalMagma_976
v0
  = case T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0 of
      C_IsInvertibleUnitalMagma'46'constructor_24571 T_IsInvertibleMagma_924
v1 T_Σ_14
v2 -> T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1
      T_IsInvertibleUnitalMagma_976
_ -> T_IsInvertibleMagma_924
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleUnitalMagma.identity
d_identity_990 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_990 :: T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 T_IsInvertibleUnitalMagma_976
v0
  = case T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0 of
      C_IsInvertibleUnitalMagma'46'constructor_24571 T_IsInvertibleMagma_924
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsInvertibleUnitalMagma_976
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverse
d_inverse_994 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_994 :: T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_inverse_994 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverseʳ
d_inverse'691'_996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_inverse'691'_996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_inverse'691'_996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'691'_996 T_IsInvertibleUnitalMagma_976
v7
du_inverse'691'_996 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'691'_996 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'691'_996 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverseˡ
d_inverse'737'_998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_inverse'737'_998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_inverse'737'_998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'737'_998 T_IsInvertibleUnitalMagma_976
v7
du_inverse'737'_998 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'737'_998 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'737'_998 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isEquivalence
d_isEquivalence_1000 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1000 :: T_IsInvertibleUnitalMagma_976 -> T_IsEquivalence_26
d_isEquivalence_1000 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isMagma
d_isMagma_1002 :: T_IsInvertibleUnitalMagma_976 -> T_IsMagma_176
d_isMagma_1002 :: T_IsInvertibleUnitalMagma_976 -> T_IsMagma_176
d_isMagma_1002 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_1004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1004 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1004 T_IsInvertibleUnitalMagma_976
v7
du_isPartialEquivalence_1004 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1004 :: T_IsInvertibleUnitalMagma_976 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1004 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.refl
d_refl_1006 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_refl_1006 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_refl_1006 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.reflexive
d_reflexive_1008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1008 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1008 T_IsInvertibleUnitalMagma_976
v7
du_reflexive_1008 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1008 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1008 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsInvertibleUnitalMagma._.setoid
d_setoid_1010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> T_Setoid_44
d_setoid_1010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7 = T_IsInvertibleUnitalMagma_976 -> T_Setoid_44
du_setoid_1010 T_IsInvertibleUnitalMagma_976
v7
du_setoid_1010 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1010 :: T_IsInvertibleUnitalMagma_976 -> T_Setoid_44
du_setoid_1010 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.sym
d_sym_1012 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1012 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1012 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.trans
d_trans_1014 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1014 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1014 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.⁻¹-cong
d_'8315''185''45'cong_1016 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1016 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1016 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_942 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-cong
d_'8729''45'cong_1018 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1018 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1018 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_1020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1020 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 T_IsInvertibleUnitalMagma_976
v7
du_'8729''45'cong'691'_1020 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_1022 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1022 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 T_IsInvertibleUnitalMagma_976
v7
du_'8729''45'cong'737'_1022 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Structures.IsInvertibleUnitalMagma.identityˡ
d_identity'737'_1024 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_identity'737'_1024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_identity'737'_1024 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'737'_1024 T_IsInvertibleUnitalMagma_976
v7
du_identity'737'_1024 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'737'_1024 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'737'_1024 T_IsInvertibleUnitalMagma_976
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsInvertibleUnitalMagma_976 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma.identityʳ
d_identity'691'_1026 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_identity'691'_1026 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_identity'691'_1026 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'691'_1026 T_IsInvertibleUnitalMagma_976
v7
du_identity'691'_1026 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'691'_1026 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'691'_1026 T_IsInvertibleUnitalMagma_976
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsInvertibleUnitalMagma_976 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma.isUnitalMagma
d_isUnitalMagma_1028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
d_isUnitalMagma_1028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> T_IsUnitalMagma_642
d_isUnitalMagma_1028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
du_isUnitalMagma_1028 T_IsInvertibleUnitalMagma_976
v7
du_isUnitalMagma_1028 ::
  T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
du_isUnitalMagma_1028 :: T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
du_isUnitalMagma_1028 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642)
-> AgdaAny -> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642
C_IsUnitalMagma'46'constructor_14317
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0)))
      ((T_IsInvertibleUnitalMagma_976 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsGroup
d_IsGroup_1036 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroup_1036 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroup_1036
  = C_IsGroup'46'constructor_26963 T_IsMonoid_686
                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsGroup.isMonoid
d_isMonoid_1050 :: T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 :: T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 T_IsGroup_1036
v0
  = case T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0 of
      C_IsGroup'46'constructor_26963 T_IsMonoid_686
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsGroup_1036
_ -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.inverse
d_inverse_1052 ::
  T_IsGroup_1036 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1052 :: T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 T_IsGroup_1036
v0
  = case T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0 of
      C_IsGroup'46'constructor_26963 T_IsMonoid_686
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsGroup_1036
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.⁻¹-cong
d_'8315''185''45'cong_1054 ::
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 T_IsGroup_1036
v0
  = case T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0 of
      C_IsGroup'46'constructor_26963 T_IsMonoid_686
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsGroup_1036
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup._.assoc
d_assoc_1058 ::
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1058 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1058 T_IsGroup_1036
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))
-- Algebra.Structures.IsGroup._.identity
d_identity_1060 ::
  T_IsGroup_1036 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1060 :: T_IsGroup_1036 -> T_Σ_14
d_identity_1060 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.identityʳ
d_identity'691'_1062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_identity'691'_1062 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_identity'691'_1062 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'691'_1062 T_IsGroup_1036
v7
du_identity'691'_1062 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'691'_1062 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'691'_1062 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.identityˡ
d_identity'737'_1064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_identity'737'_1064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_identity'737'_1064 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'737'_1064 T_IsGroup_1036
v7
du_identity'737'_1064 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'737'_1064 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'737'_1064 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.isEquivalence
d_isEquivalence_1066 ::
  T_IsGroup_1036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1066 :: T_IsGroup_1036 -> T_IsEquivalence_26
d_isEquivalence_1066 T_IsGroup_1036
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))))
-- Algebra.Structures.IsGroup._.isMagma
d_isMagma_1068 :: T_IsGroup_1036 -> T_IsMagma_176
d_isMagma_1068 :: T_IsGroup_1036 -> T_IsMagma_176
d_isMagma_1068 T_IsGroup_1036
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))
-- Algebra.Structures.IsGroup._.isPartialEquivalence
d_isPartialEquivalence_1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1070 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1070 T_IsGroup_1036
v7
du_isPartialEquivalence_1070 ::
  T_IsGroup_1036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1070 :: T_IsGroup_1036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1070 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsGroup._.isSemigroup
d_isSemigroup_1072 :: T_IsGroup_1036 -> T_IsSemigroup_472
d_isSemigroup_1072 :: T_IsGroup_1036 -> T_IsSemigroup_472
d_isSemigroup_1072 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.isUnitalMagma
d_isUnitalMagma_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> T_IsUnitalMagma_642
d_isUnitalMagma_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsUnitalMagma_642
d_isUnitalMagma_1074 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> T_IsUnitalMagma_642
du_isUnitalMagma_1074 T_IsGroup_1036
v7
du_isUnitalMagma_1074 :: T_IsGroup_1036 -> T_IsUnitalMagma_642
du_isUnitalMagma_1074 :: T_IsGroup_1036 -> T_IsUnitalMagma_642
du_isUnitalMagma_1074 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.refl
d_refl_1076 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_refl_1076 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_refl_1076 T_IsGroup_1036
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))))
-- Algebra.Structures.IsGroup._.reflexive
d_reflexive_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1078 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1078 T_IsGroup_1036
v7
du_reflexive_1078 ::
  T_IsGroup_1036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1078 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1078 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsGroup._.setoid
d_setoid_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_Setoid_44
d_setoid_1080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7 = T_IsGroup_1036 -> T_Setoid_44
du_setoid_1080 T_IsGroup_1036
v7
du_setoid_1080 ::
  T_IsGroup_1036 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1080 :: T_IsGroup_1036 -> T_Setoid_44
du_setoid_1080 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsGroup._.sym
d_sym_1082 ::
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1082 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1082 T_IsGroup_1036
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))))
-- Algebra.Structures.IsGroup._.trans
d_trans_1084 ::
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1084 :: T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1084 T_IsGroup_1036
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))))
-- Algebra.Structures.IsGroup._.∙-cong
d_'8729''45'cong_1086 ::
  T_IsGroup_1036 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1086 :: T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1086 T_IsGroup_1036
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))))
-- Algebra.Structures.IsGroup._.∙-congʳ
d_'8729''45'cong'691'_1088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1088 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1088 T_IsGroup_1036
v7
du_'8729''45'cong'691'_1088 ::
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1088 :: T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1088 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsGroup._.∙-congˡ
d_'8729''45'cong'737'_1090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1090 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1090 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1090 T_IsGroup_1036
v7
du_'8729''45'cong'737'_1090 ::
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1090 :: T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1090 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsGroup._\\_
d__'92''92'__1092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__1092 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'92''92'__1092 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~T_IsGroup_1036
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1092 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v8 AgdaAny
v9
du__'92''92'__1092 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1092 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1092 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 = (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1 AgdaAny
v2) AgdaAny
v3
-- Algebra.Structures.IsGroup._//_
d__'47''47'__1098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__1098 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~T_IsGroup_1036
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v8 AgdaAny
v9
du__'47''47'__1098 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 = (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1 AgdaAny
v3)
-- Algebra.Structures.IsGroup._-_
d__'45'__1104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'45'__1104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~T_IsGroup_1036
v7 = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1104 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'45'__1104 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1104 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1104 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsGroup.inverseˡ
d_inverse'737'_1106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_inverse'737'_1106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_inverse'737'_1106 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 T_IsGroup_1036
v7
du_inverse'737'_1106 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 T_IsGroup_1036
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup.inverseʳ
d_inverse'691'_1108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_inverse'691'_1108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_inverse'691'_1108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 T_IsGroup_1036
v7
du_inverse'691'_1108 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 T_IsGroup_1036
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1114 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
du_unique'737''45''8315''185'_1114 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1114 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_1036
v3
  = (T_Setoid_44
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_44
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_assoc'8743'id'8743'inv'691''8658'inv'737''45'unique_456
      (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))
-- Algebra.Structures.IsGroup.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1120 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
du_unique'691''45''8315''185'_1120 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1120 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_1036
v3
  = (T_Setoid_44
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_44
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_assoc'8743'id'8743'inv'737''8658'inv'691''45'unique_476
      (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))
-- Algebra.Structures.IsGroup.isInvertibleMagma
d_isInvertibleMagma_1122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1122 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_1122 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 T_IsGroup_1036
v7
du_isInvertibleMagma_1122 ::
  T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 :: T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 T_IsGroup_1036
v0
  = (T_IsMagma_176
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      T_IsMagma_176
-> T_Σ_14
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
C_IsInvertibleMagma'46'constructor_22695
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))))
      ((T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1124 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1124 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
  = T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 T_IsGroup_1036
v7
du_isInvertibleUnitalMagma_1124 ::
  T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 :: T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 T_IsGroup_1036
v0
  = (T_IsInvertibleMagma_924
 -> T_Σ_14 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> T_Σ_14 -> T_IsInvertibleUnitalMagma_976
C_IsInvertibleUnitalMagma'46'constructor_24571
      ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))
-- Algebra.Structures.IsAbelianGroup
d_IsAbelianGroup_1132 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsAbelianGroup_1132 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsAbelianGroup_1132
  = C_IsAbelianGroup'46'constructor_32441 T_IsGroup_1036
                                          (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsAbelianGroup.isGroup
d_isGroup_1144 :: T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 :: T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 T_IsAbelianGroup_1132
v0
  = case T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0 of
      C_IsAbelianGroup'46'constructor_32441 T_IsGroup_1036
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1
      T_IsAbelianGroup_1132
_ -> T_IsGroup_1036
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup.comm
d_comm_1146 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 T_IsAbelianGroup_1132
v0
  = case T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0 of
      C_IsAbelianGroup'46'constructor_32441 T_IsGroup_1036
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsAbelianGroup_1132
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup._._//_
d__'47''47'__1150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__1150 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~T_IsAbelianGroup_1132
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1150 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'47''47'__1150 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1150 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1150 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsAbelianGroup._.assoc
d_assoc_1152 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1152 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1152 T_IsAbelianGroup_1132
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))
-- Algebra.Structures.IsAbelianGroup._.identity
d_identity_1154 ::
  T_IsAbelianGroup_1132 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1154 :: T_IsAbelianGroup_1132 -> T_Σ_14
d_identity_1154 T_IsAbelianGroup_1132
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))
-- Algebra.Structures.IsAbelianGroup._.identityʳ
d_identity'691'_1156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_identity'691'_1156 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_identity'691'_1156 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'691'_1156 T_IsAbelianGroup_1132
v7
du_identity'691'_1156 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'691'_1156 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'691'_1156 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Structures.IsAbelianGroup._.identityˡ
d_identity'737'_1158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_identity'737'_1158 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_identity'737'_1158 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'737'_1158 T_IsAbelianGroup_1132
v7
du_identity'737'_1158 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'737'_1158 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'737'_1158 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Structures.IsAbelianGroup._.inverse
d_inverse_1160 ::
  T_IsAbelianGroup_1132 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1160 :: T_IsAbelianGroup_1132 -> T_Σ_14
d_inverse_1160 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseʳ
d_inverse'691'_1162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_inverse'691'_1162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_inverse'691'_1162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'691'_1162 T_IsAbelianGroup_1132
v7
du_inverse'691'_1162 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'691'_1162 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'691'_1162 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseˡ
d_inverse'737'_1164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_inverse'737'_1164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_inverse'737'_1164 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'737'_1164 T_IsAbelianGroup_1132
v7
du_inverse'737'_1164 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'737'_1164 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'737'_1164 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isEquivalence
d_isEquivalence_1166 ::
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1166 :: T_IsAbelianGroup_1132 -> T_IsEquivalence_26
d_isEquivalence_1166 T_IsAbelianGroup_1132
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))))
-- Algebra.Structures.IsAbelianGroup._.isInvertibleMagma
d_isInvertibleMagma_1168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1168 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_1168 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1168 T_IsAbelianGroup_1132
v7
du_isInvertibleMagma_1168 ::
  T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1168 :: T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1168 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_IsInvertibleMagma_924)
-> AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1170 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1170 T_IsAbelianGroup_1132
v7
du_isInvertibleUnitalMagma_1170 ::
  T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1170 :: T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1170 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isMagma
d_isMagma_1172 :: T_IsAbelianGroup_1132 -> T_IsMagma_176
d_isMagma_1172 :: T_IsAbelianGroup_1132 -> T_IsMagma_176
d_isMagma_1172 T_IsAbelianGroup_1132
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))
-- Algebra.Structures.IsAbelianGroup._.isMonoid
d_isMonoid_1174 :: T_IsAbelianGroup_1132 -> T_IsMonoid_686
d_isMonoid_1174 :: T_IsAbelianGroup_1132 -> T_IsMonoid_686
d_isMonoid_1174 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isPartialEquivalence
d_isPartialEquivalence_1176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1176 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1176 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 T_IsAbelianGroup_1132
v7
du_isPartialEquivalence_1176 ::
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 :: T_IsAbelianGroup_1132 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsAbelianGroup._.isSemigroup
d_isSemigroup_1178 :: T_IsAbelianGroup_1132 -> T_IsSemigroup_472
d_isSemigroup_1178 :: T_IsAbelianGroup_1132 -> T_IsSemigroup_472
d_isSemigroup_1178 T_IsAbelianGroup_1132
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))
-- Algebra.Structures.IsAbelianGroup._.isUnitalMagma
d_isUnitalMagma_1180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
d_isUnitalMagma_1180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsUnitalMagma_642
d_isUnitalMagma_1180 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
du_isUnitalMagma_1180 T_IsAbelianGroup_1132
v7
du_isUnitalMagma_1180 ::
  T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
du_isUnitalMagma_1180 :: T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
du_isUnitalMagma_1180 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Structures.IsAbelianGroup._.refl
d_refl_1182 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_refl_1182 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_refl_1182 T_IsAbelianGroup_1132
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))))
-- Algebra.Structures.IsAbelianGroup._.reflexive
d_reflexive_1184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1184 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1184 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1184 T_IsAbelianGroup_1132
v7
du_reflexive_1184 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1184 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1184 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsAbelianGroup._.setoid
d_setoid_1186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1186 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_Setoid_44
d_setoid_1186 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7 = T_IsAbelianGroup_1132 -> T_Setoid_44
du_setoid_1186 T_IsAbelianGroup_1132
v7
du_setoid_1186 ::
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1186 :: T_IsAbelianGroup_1132 -> T_Setoid_44
du_setoid_1186 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsAbelianGroup._.sym
d_sym_1188 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1188 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1188 T_IsAbelianGroup_1132
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))))
-- Algebra.Structures.IsAbelianGroup._.trans
d_trans_1190 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1190 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1190 T_IsAbelianGroup_1132
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))))
-- Algebra.Structures.IsAbelianGroup._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1192 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1192 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
du_unique'691''45''8315''185'_1192 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1192 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1192 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_1132
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3))
-- Algebra.Structures.IsAbelianGroup._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1194 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1194 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
du_unique'737''45''8315''185'_1194 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1194 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1194 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_1132
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3))
-- Algebra.Structures.IsAbelianGroup._.⁻¹-cong
d_'8315''185''45'cong_1196 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1196 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1196 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.∙-cong
d_'8729''45'cong_1198 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1198 :: T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1198 T_IsAbelianGroup_1132
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))))
-- Algebra.Structures.IsAbelianGroup._.∙-congʳ
d_'8729''45'cong'691'_1200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1200 T_IsAbelianGroup_1132
v7
du_'8729''45'cong'691'_1200 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1200 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1200 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsAbelianGroup._.∙-congˡ
d_'8729''45'cong'737'_1202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1202 T_IsAbelianGroup_1132
v7
du_'8729''45'cong'737'_1202 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1202 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1202 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsAbelianGroup.isCommutativeMonoid
d_isCommutativeMonoid_1204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1204 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1204 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 T_IsAbelianGroup_1132
v7
du_isCommutativeMonoid_1204 ::
  T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 :: T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 T_IsAbelianGroup_1132
v0
  = (T_IsMonoid_686
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_736
C_IsCommutativeMonoid'46'constructor_17695
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))
      ((T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeMagma
d_isCommutativeMagma_1208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1208 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1208 T_IsAbelianGroup_1132
v7
du_isCommutativeMagma_1208 ::
  T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1208 :: T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1208 T_IsAbelianGroup_1132
v0
  = let v1 :: t
v1 = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeSemigroup
d_isCommutativeSemigroup_1210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1210 T_IsAbelianGroup_1132
v7
du_isCommutativeSemigroup_1210 ::
  T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1210 :: T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1210 T_IsAbelianGroup_1132
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsNearSemiring
d_IsNearSemiring_1218 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiring_1218 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiring_1218
  = C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
                                          (AgdaAny ->
                                           AgdaAny ->
                                           AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsNearSemiring.+-isMonoid
d_'43''45'isMonoid_1236 :: T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 :: T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsNearSemiring_1218
_ -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.*-cong
d_'42''45'cong_1238 ::
  T_IsNearSemiring_1218 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1238 :: T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1238 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsNearSemiring_1218
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.*-assoc
d_'42''45'assoc_1240 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1240 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1240 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsNearSemiring_1218
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.distribʳ
d_distrib'691'_1242 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1242 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1242 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsNearSemiring_1218
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.zeroˡ
d_zero'737'_1244 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_zero'737'_1244 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_zero'737'_1244 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_IsNearSemiring_1218
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring._.assoc
d_assoc_1248 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1248 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1248 T_IsNearSemiring_1218
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))
-- Algebra.Structures.IsNearSemiring._.∙-cong
d_'8729''45'cong_1250 ::
  T_IsNearSemiring_1218 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1250 :: T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1250 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1252 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1252 T_IsNearSemiring_1218
v7
du_'8729''45'cong'691'_1252 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1252 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1252 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1254 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1254 T_IsNearSemiring_1218
v7
du_'8729''45'cong'737'_1254 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1254 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1254 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsNearSemiring._.identity
d_identity_1256 ::
  T_IsNearSemiring_1218 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1256 :: T_IsNearSemiring_1218 -> T_Σ_14
d_identity_1256 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.identityʳ
d_identity'691'_1258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_identity'691'_1258 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
d_identity'691'_1258 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'691'_1258 T_IsNearSemiring_1218
v7
du_identity'691'_1258 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'691'_1258 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'691'_1258 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.identityˡ
d_identity'737'_1260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_identity'737'_1260 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
d_identity'737'_1260 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'737'_1260 T_IsNearSemiring_1218
v7
du_identity'737'_1260 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'737'_1260 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'737'_1260 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.isMagma
d_isMagma_1262 :: T_IsNearSemiring_1218 -> T_IsMagma_176
d_isMagma_1262 :: T_IsNearSemiring_1218 -> T_IsMagma_176
d_isMagma_1262 T_IsNearSemiring_1218
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))
-- Algebra.Structures.IsNearSemiring._.isSemigroup
d_isSemigroup_1264 :: T_IsNearSemiring_1218 -> T_IsSemigroup_472
d_isSemigroup_1264 :: T_IsNearSemiring_1218 -> T_IsSemigroup_472
d_isSemigroup_1264 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.isUnitalMagma
d_isUnitalMagma_1266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsNearSemiring_1218 -> T_IsUnitalMagma_642
d_isUnitalMagma_1266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsUnitalMagma_642
d_isUnitalMagma_1266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> T_IsUnitalMagma_642
du_isUnitalMagma_1266 T_IsNearSemiring_1218
v7
du_isUnitalMagma_1266 ::
  T_IsNearSemiring_1218 -> T_IsUnitalMagma_642
du_isUnitalMagma_1266 :: T_IsNearSemiring_1218 -> T_IsUnitalMagma_642
du_isUnitalMagma_1266 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.isEquivalence
d_isEquivalence_1268 ::
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1268 :: T_IsNearSemiring_1218 -> T_IsEquivalence_26
d_isEquivalence_1268 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))))
-- Algebra.Structures.IsNearSemiring._.isPartialEquivalence
d_isPartialEquivalence_1270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1270 T_IsNearSemiring_1218
v7
du_isPartialEquivalence_1270 ::
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1270 :: T_IsNearSemiring_1218 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1270 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsNearSemiring._.refl
d_refl_1272 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_refl_1272 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_refl_1272 T_IsNearSemiring_1218
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
-- Algebra.Structures.IsNearSemiring._.reflexive
d_reflexive_1274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_1218 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1274 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1274 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1274 T_IsNearSemiring_1218
v7
du_reflexive_1274 ::
  T_IsNearSemiring_1218 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1274 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1274 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsNearSemiring._.setoid
d_setoid_1276 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_Setoid_44
d_setoid_1276 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7 = T_IsNearSemiring_1218 -> T_Setoid_44
du_setoid_1276 T_IsNearSemiring_1218
v7
du_setoid_1276 ::
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1276 :: T_IsNearSemiring_1218 -> T_Setoid_44
du_setoid_1276 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsNearSemiring._.sym
d_sym_1278 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1278 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1278 T_IsNearSemiring_1218
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
-- Algebra.Structures.IsNearSemiring._.trans
d_trans_1280 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1280 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1280 T_IsNearSemiring_1218
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
-- Algebra.Structures.IsNearSemiring.*-isMagma
d_'42''45'isMagma_1282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsNearSemiring_1218 -> T_IsMagma_176
d_'42''45'isMagma_1282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsMagma_176
d_'42''45'isMagma_1282 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 T_IsNearSemiring_1218
v7
du_'42''45'isMagma_1282 :: T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 :: T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 T_IsNearSemiring_1218
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
      ((T_IsNearSemiring_1218
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1238 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring.*-isSemigroup
d_'42''45'isSemigroup_1284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsNearSemiring_1218 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1284 T_IsNearSemiring_1218
v7
du_'42''45'isSemigroup_1284 ::
  T_IsNearSemiring_1218 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1284 :: T_IsNearSemiring_1218 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1284 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
C_IsSemigroup'46'constructor_10417
      ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
      ((T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1240 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1288 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1288 T_IsNearSemiring_1218
v7
du_'8729''45'cong'691'_1288 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1288 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1288 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1290 T_IsNearSemiring_1218
v7
du_'8729''45'cong'737'_1290 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1290 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1290 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsSemiringWithoutOne
d_IsSemiringWithoutOne_1298 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringWithoutOne_1298 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringWithoutOne_1298
  = C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
                                                (AgdaAny ->
                                                 AgdaAny ->
                                                 AgdaAny ->
                                                 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1316 ::
  T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 :: T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1
      T_IsSemiringWithoutOne_1298
_ -> T_IsCommutativeMonoid_736
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.*-cong
d_'42''45'cong_1318 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1318 :: T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemiringWithoutOne_1298
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.*-assoc
d_'42''45'assoc_1320 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsSemiringWithoutOne_1298
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.distrib
d_distrib_1322 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1322 :: T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_distrib_1322 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsSemiringWithoutOne_1298
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.zero
d_zero_1324 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1324 :: T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v5
      T_IsSemiringWithoutOne_1298
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne._.comm
d_comm_1328 ::
  T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1328 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1328 T_IsSemiringWithoutOne_1298
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1330 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1330 T_IsSemiringWithoutOne_1298
v7
du_isCommutativeMagma_1330 ::
  T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1330 :: T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1330 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1332 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1332 T_IsSemiringWithoutOne_1298
v7
du_isCommutativeSemigroup_1332 ::
  T_IsSemiringWithoutOne_1298 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1332 :: T_IsSemiringWithoutOne_1298 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1332 T_IsSemiringWithoutOne_1298
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isMonoid
d_isMonoid_1334 :: T_IsSemiringWithoutOne_1298 -> T_IsMonoid_686
d_isMonoid_1334 :: T_IsSemiringWithoutOne_1298 -> T_IsMonoid_686
d_isMonoid_1334 T_IsSemiringWithoutOne_1298
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.setoid
d_setoid_1336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1336 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_Setoid_44
d_setoid_1336 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7 = T_IsSemiringWithoutOne_1298 -> T_Setoid_44
du_setoid_1336 T_IsSemiringWithoutOne_1298
v7
du_setoid_1336 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1336 :: T_IsSemiringWithoutOne_1298 -> T_Setoid_44
du_setoid_1336 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutOne._._≈_
d__'8776'__1340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1340 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsSemiringWithoutOne._._≉_
d__'8777'__1342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1342 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1342 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsSemiringWithoutOne._.Carrier
d_Carrier_1344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> ()
d_Carrier_1344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_Level_18
d_Carrier_1344 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsSemiringWithoutOne._.isEquivalence
d_isEquivalence_1346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsEquivalence_26
d_isEquivalence_1346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsEquivalence_26
du_isEquivalence_1346 T_IsSemiringWithoutOne_1298
v7
du_isEquivalence_1346 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1346 :: T_IsSemiringWithoutOne_1298 -> T_IsEquivalence_26
du_isEquivalence_1346 T_IsSemiringWithoutOne_1298
v0
  = (T_Setoid_44 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
      (let v1 :: T_IsMonoid_686
v1
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))))
-- Algebra.Structures.IsSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1348 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1348 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1348 T_IsSemiringWithoutOne_1298
v7
du_isPartialEquivalence_1348 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1348 :: T_IsSemiringWithoutOne_1298 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1348 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: b
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> b
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.partialSetoid
d_partialSetoid_1350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_PartialSetoid_10
d_partialSetoid_1350 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_PartialSetoid_10
du_partialSetoid_1350 T_IsSemiringWithoutOne_1298
v7
du_partialSetoid_1350 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1350 :: T_IsSemiringWithoutOne_1298 -> T_PartialSetoid_10
du_partialSetoid_1350 T_IsSemiringWithoutOne_1298
v0
  = (T_Setoid_44 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
      (let v1 :: T_IsMonoid_686
v1
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))))
-- Algebra.Structures.IsSemiringWithoutOne._.refl
d_refl_1352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
d_refl_1352 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
d_refl_1352 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7 = T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_refl_1352 T_IsSemiringWithoutOne_1298
v7
du_refl_1352 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_refl_1352 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_refl_1352 T_IsSemiringWithoutOne_1298
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
         (let v1 :: T_IsMonoid_686
v1
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))))
-- Algebra.Structures.IsSemiringWithoutOne._.reflexive
d_reflexive_1354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1354 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1354 T_IsSemiringWithoutOne_1298
v7
du_reflexive_1354 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1354 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1354 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: b
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> b
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))
           AgdaAny
v2)
-- Algebra.Structures.IsSemiringWithoutOne._.sym
d_sym_1356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7 = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1356 T_IsSemiringWithoutOne_1298
v7
du_sym_1356 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1356 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1356 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: b
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> b
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.trans
d_trans_1358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1358 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1358 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7 = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1358 T_IsSemiringWithoutOne_1298
v7
du_trans_1358 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1358 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1358 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: b
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> b
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsSemiringWithoutOne.*-isMagma
d_'42''45'isMagma_1360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
d_'42''45'isMagma_1360 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsMagma_176
d_'42''45'isMagma_1360 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 T_IsSemiringWithoutOne_1298
v7
du_'42''45'isMagma_1360 ::
  T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 :: T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 T_IsSemiringWithoutOne_1298
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
         (let v1 :: T_IsSemigroup_472
v1
                = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
                    ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
                       T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                       ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_1362 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1362 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1362 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362 T_IsSemiringWithoutOne_1298
v7
du_'42''45'isSemigroup_1362 ::
  T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362 :: T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
C_IsSemigroup'46'constructor_10417
      ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1366 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1366 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1366 T_IsSemiringWithoutOne_1298
v7
du_'8729''45'cong'691'_1366 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1366 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1366 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1368 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1368 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1368 T_IsSemiringWithoutOne_1298
v7
du_'8729''45'cong'737'_1368 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1368 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1368 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroˡ
d_zero'737'_1370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
d_zero'737'_1370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
d_zero'737'_1370 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 T_IsSemiringWithoutOne_1298
v7
du_zero'737'_1370 ::
  T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 T_IsSemiringWithoutOne_1298
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 ((T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroʳ
d_zero'691'_1372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
d_zero'691'_1372 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
d_zero'691'_1372 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 T_IsSemiringWithoutOne_1298
v7
du_zero'691'_1372 ::
  T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 T_IsSemiringWithoutOne_1298
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 ((T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.isNearSemiring
d_isNearSemiring_1374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
d_isNearSemiring_1374 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsNearSemiring_1218
d_isNearSemiring_1374 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 T_IsSemiringWithoutOne_1298
v7
du_isNearSemiring_1374 ::
  T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 :: T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMonoid_686
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsNearSemiring_1218)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsNearSemiring_1218
forall a b. a -> b
coe
      T_IsMonoid_686
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiring_1218
C_IsNearSemiring'46'constructor_35025
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
      ((T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_distrib_1322 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)))
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_1382 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemiringWithoutOne_1382 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsCommutativeSemiringWithoutOne_1382
  = C_IsCommutativeSemiringWithoutOne'46'constructor_41457 T_IsSemiringWithoutOne_1298
                                                           (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_1394 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 :: T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 T_IsCommutativeSemiringWithoutOne_1382
v0
  = case T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0 of
      C_IsCommutativeSemiringWithoutOne'46'constructor_41457 T_IsSemiringWithoutOne_1298
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
        -> T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1
      T_IsCommutativeSemiringWithoutOne_1382
_ -> T_IsSemiringWithoutOne_1298
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_1396 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1396 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1396 T_IsCommutativeSemiringWithoutOne_1382
v0
  = case T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0 of
      C_IsCommutativeSemiringWithoutOne'46'constructor_41457 T_IsSemiringWithoutOne_1298
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemiringWithoutOne_1382
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._._≈_
d__'8776'__1400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1400 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._._≉_
d__'8777'__1402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1402 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1402 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-assoc
d_'42''45'assoc_1404 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1404 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1404 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-cong
d_'42''45'cong_1406 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1406 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1406 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1408 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1408 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1408 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'8729''45'cong'691'_1408 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1408 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1408 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1410 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1410 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1410 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'8729''45'cong'737'_1410 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1410 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1410 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-isMagma
d_'42''45'isMagma_1412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMagma_176
d_'42''45'isMagma_1412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsMagma_176
d_'42''45'isMagma_1412 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMagma_176
du_'42''45'isMagma_1412 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'42''45'isMagma_1412 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMagma_176
du_'42''45'isMagma_1412 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMagma_176
du_'42''45'isMagma_1412 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_1414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1414 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1414 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1414 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'42''45'isSemigroup_1414 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1414 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1414 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.comm
d_comm_1416 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1416 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1416 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1418 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isCommutativeMagma_1418 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1418 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1418 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1420 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1420 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1420 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1422 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1422 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isCommutativeSemigroup_1422 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1422 :: T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1422 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isMonoid
d_isMonoid_1424 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMonoid_686
d_isMonoid_1424 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMonoid_686
d_isMonoid_1424 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.Carrier
d_Carrier_1426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382 -> ()
d_Carrier_1426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_Level_18
d_Carrier_1426 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.distrib
d_distrib_1428 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1428 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_Σ_14
d_distrib_1428 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_distrib_1322 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isEquivalence
d_isEquivalence_1430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsEquivalence_26
d_isEquivalence_1430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsEquivalence_26
du_isEquivalence_1430 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isEquivalence_1430 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1430 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsEquivalence_26
du_isEquivalence_1430 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
         (let v2 :: T_IsMonoid_686
v2
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isNearSemiring
d_isNearSemiring_1432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsNearSemiring_1218
d_isNearSemiring_1432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsNearSemiring_1218
d_isNearSemiring_1432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsNearSemiring_1218
du_isNearSemiring_1432 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isNearSemiring_1432 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsNearSemiring_1218
du_isNearSemiring_1432 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsNearSemiring_1218
du_isNearSemiring_1432 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1434 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1434 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1434 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1434 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isPartialEquivalence_1434 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1434 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1434 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.partialSetoid
d_partialSetoid_1436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1436 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_PartialSetoid_10
d_partialSetoid_1436 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_PartialSetoid_10
du_partialSetoid_1436 T_IsCommutativeSemiringWithoutOne_1382
v7
du_partialSetoid_1436 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1436 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_PartialSetoid_10
du_partialSetoid_1436 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         (let v2 :: T_IsMonoid_686
v2
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.refl
d_refl_1438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
d_refl_1438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
d_refl_1438 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_refl_1438 T_IsCommutativeSemiringWithoutOne_1382
v7
du_refl_1438 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_refl_1438 :: T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_refl_1438 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
            (let v2 :: T_IsMonoid_686
v2
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                       ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.reflexive
d_reflexive_1440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1440 T_IsCommutativeSemiringWithoutOne_1382
v7
du_reflexive_1440 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1440 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1440 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.setoid
d_setoid_1442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_Setoid_44
d_setoid_1442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382 -> T_Setoid_44
du_setoid_1442 T_IsCommutativeSemiringWithoutOne_1382
v7
du_setoid_1442 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1442 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_Setoid_44
du_setoid_1442 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.sym
d_sym_1444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1444 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1444 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1444 T_IsCommutativeSemiringWithoutOne_1382
v7
du_sym_1444 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1444 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1444 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.trans
d_trans_1446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1446 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1446 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1446 T_IsCommutativeSemiringWithoutOne_1382
v7
du_trans_1446 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1446 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1446 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zero
d_zero_1448 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1448 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_Σ_14
d_zero_1448 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zeroʳ
d_zero'691'_1450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
d_zero'691'_1450 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
d_zero'691'_1450 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'691'_1450 T_IsCommutativeSemiringWithoutOne_1382
v7
du_zero'691'_1450 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'691'_1450 :: T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'691'_1450 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zeroˡ
d_zero'737'_1452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
d_zero'737'_1452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
d_zero'737'_1452 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'737'_1452 T_IsCommutativeSemiringWithoutOne_1382
v7
du_zero'737'_1452 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'737'_1452 :: T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'737'_1452 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1454 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1454 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                      T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'42''45'isCommutativeSemigroup_1454 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 :: T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemigroup_472
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548
C_IsCommutativeSemigroup'46'constructor_12093
      ((T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0)))
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1396 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1458 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1458 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isCommutativeMagma_1458 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1458 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1458 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero
d_IsSemiringWithoutAnnihilatingZero_1468 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringWithoutAnnihilatingZero_1468 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7
  = ()
data T_IsSemiringWithoutAnnihilatingZero_1468
  = C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
                                                             (AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny -> AgdaAny -> AgdaAny)
                                                             (AgdaAny ->
                                                              AgdaAny -> AgdaAny -> AgdaAny)
                                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1488 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> T_IsCommutativeMonoid_736
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-cong
d_'42''45'cong_1490 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1490 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-assoc
d_'42''45'assoc_1492 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-identity
d_'42''45'identity_1494 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1494 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distrib
d_distrib_1496 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1496 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v5
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distribˡ
d_distrib'737'_1498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1498 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1498 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_distrib'737'_1498 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distribʳ
d_distrib'691'_1500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1500 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1500 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_distrib'691'_1500 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.assoc
d_assoc_1504 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1504 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1504 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.comm
d_comm_1506 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1506 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1506 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-cong
d_'8729''45'cong_1508 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1508 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1508 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_1510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1510 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1510 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1510 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'8729''45'cong'691'_1510 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1510 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1510 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_1512 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1512 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1512 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1512 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'8729''45'cong'737'_1512 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1512 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1512 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identity
d_identity_1514 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1514 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_identity_1514 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_1516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_identity'691'_1516 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
d_identity'691'_1516 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1516 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_identity'691'_1516 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1516 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1516 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_1518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_identity'737'_1518 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
d_identity'737'_1518 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1518 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_identity'737'_1518 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1518 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1518 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isCommutativeMagma
d_isCommutativeMagma_1520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeMagma_212
d_isCommutativeMagma_1520 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1520 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1520 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isCommutativeMagma_1520 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeMagma_212
du_isCommutativeMagma_1520 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1520 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isCommutativeSemigroup
d_isCommutativeSemigroup_1522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1522 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1522 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1522 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isCommutativeSemigroup_1522 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1522 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1522 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isMagma
d_isMagma_1524 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
d_isMagma_1524 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
d_isMagma_1524 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isMonoid
d_isMonoid_1526 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
d_isMonoid_1526 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
d_isMonoid_1526 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isSemigroup
d_isSemigroup_1528 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
d_isSemigroup_1528 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
d_isSemigroup_1528 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isUnitalMagma
d_isUnitalMagma_1530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
d_isUnitalMagma_1530 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsUnitalMagma_642
d_isUnitalMagma_1530 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
du_isUnitalMagma_1530 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isUnitalMagma_1530 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
du_isUnitalMagma_1530 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
du_isUnitalMagma_1530 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isEquivalence
d_isEquivalence_1532 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1532 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsEquivalence_26
d_isEquivalence_1532 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isPartialEquivalence
d_isPartialEquivalence_1534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1534 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1534 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1534 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isPartialEquivalence_1534 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1534 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1534 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.refl
d_refl_1536 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_refl_1536 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_refl_1536 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.reflexive
d_reflexive_1538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1538 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1538 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1538 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_reflexive_1538 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1538 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1538 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.setoid
d_setoid_1540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1540 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_Setoid_44
d_setoid_1540 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Setoid_44
du_setoid_1540 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_setoid_1540 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1540 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Setoid_44
du_setoid_1540 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.sym
d_sym_1542 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1542 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1542 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.trans
d_trans_1544 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1544 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1544 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-isMagma
d_'42''45'isMagma_1546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
d_'42''45'isMagma_1546 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsMagma_176
d_'42''45'isMagma_1546 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'42''45'isMagma_1546 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-isSemigroup
d_'42''45'isSemigroup_1548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1548 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'42''45'isSemigroup_1548 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
C_IsSemigroup'46'constructor_10417
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-isMonoid
d_'42''45'isMonoid_1550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
d_'42''45'isMonoid_1550 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsMonoid_686
d_'42''45'isMonoid_1550 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'42''45'isMonoid_1550 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
C_IsMonoid'46'constructor_15873
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_1554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1554 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1554 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1554 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'8729''45'cong'691'_1554 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1554 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1554 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_1556 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1556 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1556 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1556 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'8729''45'cong'737'_1556 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1556 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1556 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_1558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_identity'691'_1558 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
d_identity'691'_1558 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1558 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_identity'691'_1558 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1558 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1558 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_1560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_identity'737'_1560 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
d_identity'737'_1560 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1560 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_identity'737'_1560 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1560 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1560 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiring
d_IsSemiring_1570 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiring_1570 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsSemiring_1570
  = C_IsSemiring'46'constructor_48071 T_IsSemiringWithoutAnnihilatingZero_1468
                                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1584 ::
  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 :: T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 T_IsSemiring_1570
v0
  = case T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0 of
      C_IsSemiring'46'constructor_48071 T_IsSemiringWithoutAnnihilatingZero_1468
v1 T_Σ_14
v2 -> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1
      T_IsSemiring_1570
_ -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiring.zero
d_zero_1586 ::
  T_IsSemiring_1570 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1586 :: T_IsSemiring_1570 -> T_Σ_14
d_zero_1586 T_IsSemiring_1570
v0
  = case T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0 of
      C_IsSemiring'46'constructor_48071 T_IsSemiringWithoutAnnihilatingZero_1468
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsSemiring_1570
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiring._.*-assoc
d_'42''45'assoc_1590 ::
  T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1590 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1590 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.*-cong
d_'42''45'cong_1592 ::
  T_IsSemiring_1570 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1592 :: T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1592 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.∙-congʳ
d_'8729''45'cong'691'_1594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1594 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1594 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1594 T_IsSemiring_1570
v8
du_'8729''45'cong'691'_1594 ::
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1594 :: T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1594 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiring._.∙-congˡ
d_'8729''45'cong'737'_1596 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1596 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1596 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1596 T_IsSemiring_1570
v8
du_'8729''45'cong'737'_1596 ::
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1596 :: T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1596 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiring._.*-identity
d_'42''45'identity_1598 ::
  T_IsSemiring_1570 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1598 :: T_IsSemiring_1570 -> T_Σ_14
d_'42''45'identity_1598 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.identityʳ
d_identity'691'_1600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_identity'691'_1600 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
d_identity'691'_1600 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'691'_1600 T_IsSemiring_1570
v8
du_identity'691'_1600 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'691'_1600 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'691'_1600 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1)))
-- Algebra.Structures.IsSemiring._.identityˡ
d_identity'737'_1602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_identity'737'_1602 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
d_identity'737'_1602 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'737'_1602 T_IsSemiring_1570
v8
du_identity'737'_1602 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'737'_1602 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'737'_1602 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1)))
-- Algebra.Structures.IsSemiring._.*-isMagma
d_'42''45'isMagma_1604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> T_IsMagma_176
d_'42''45'isMagma_1604 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsMagma_176
d_'42''45'isMagma_1604 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsMagma_176
du_'42''45'isMagma_1604 T_IsSemiring_1570
v8
du_'42''45'isMagma_1604 :: T_IsSemiring_1570 -> T_IsMagma_176
du_'42''45'isMagma_1604 :: T_IsSemiring_1570 -> T_IsMagma_176
du_'42''45'isMagma_1604 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.*-isMonoid
d_'42''45'isMonoid_1606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> T_IsMonoid_686
d_'42''45'isMonoid_1606 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsMonoid_686
d_'42''45'isMonoid_1606 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsMonoid_686
du_'42''45'isMonoid_1606 T_IsSemiring_1570
v8
du_'42''45'isMonoid_1606 :: T_IsSemiring_1570 -> T_IsMonoid_686
du_'42''45'isMonoid_1606 :: T_IsSemiring_1570 -> T_IsMonoid_686
du_'42''45'isMonoid_1606 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.*-isSemigroup
d_'42''45'isSemigroup_1608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1608 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1608 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1608 T_IsSemiring_1570
v8
du_'42''45'isSemigroup_1608 ::
  T_IsSemiring_1570 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1608 :: T_IsSemiring_1570 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1608 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.assoc
d_assoc_1610 ::
  T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1610 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1610 T_IsSemiring_1570
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))))
-- Algebra.Structures.IsSemiring._.comm
d_comm_1612 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1612 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1612 T_IsSemiring_1570
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))
-- Algebra.Structures.IsSemiring._.∙-cong
d_'8729''45'cong_1614 ::
  T_IsSemiring_1570 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1614 :: T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1614 T_IsSemiring_1570
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))))))
-- Algebra.Structures.IsSemiring._.∙-congʳ
d_'8729''45'cong'691'_1616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1616 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1616 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1616 T_IsSemiring_1570
v8
du_'8729''45'cong'691'_1616 ::
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1616 :: T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1616 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsSemiring._.∙-congˡ
d_'8729''45'cong'737'_1618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1618 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1618 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1618 T_IsSemiring_1570
v8
du_'8729''45'cong'737'_1618 ::
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1618 :: T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1618 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsSemiring._.identity
d_identity_1620 ::
  T_IsSemiring_1570 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1620 :: T_IsSemiring_1570 -> T_Σ_14
d_identity_1620 T_IsSemiring_1570
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))))
-- Algebra.Structures.IsSemiring._.identityʳ
d_identity'691'_1622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_identity'691'_1622 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
d_identity'691'_1622 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'691'_1622 T_IsSemiring_1570
v8
du_identity'691'_1622 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'691'_1622 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'691'_1622 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Structures.IsSemiring._.identityˡ
d_identity'737'_1624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_identity'737'_1624 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
d_identity'737'_1624 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'737'_1624 T_IsSemiring_1570
v8
du_identity'737'_1624 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'737'_1624 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_identity'737'_1624 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Structures.IsSemiring._.isCommutativeMagma
d_isCommutativeMagma_1626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1626 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1626 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1626 T_IsSemiring_1570
v8
du_isCommutativeMagma_1626 ::
  T_IsSemiring_1570 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1626 :: T_IsSemiring_1570 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1626 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Structures.IsSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1628 ::
  T_IsSemiring_1570 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1628 :: T_IsSemiring_1570 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1628 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_1630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsSemiring_1570 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1630 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1630 T_IsSemiring_1570
v8
du_isCommutativeSemigroup_1630 ::
  T_IsSemiring_1570 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1630 :: T_IsSemiring_1570 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1630 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1)))
-- Algebra.Structures.IsSemiring._.isMagma
d_isMagma_1632 :: T_IsSemiring_1570 -> T_IsMagma_176
d_isMagma_1632 :: T_IsSemiring_1570 -> T_IsMagma_176
d_isMagma_1632 T_IsSemiring_1570
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))))
-- Algebra.Structures.IsSemiring._.isMonoid
d_isMonoid_1634 :: T_IsSemiring_1570 -> T_IsMonoid_686
d_isMonoid_1634 :: T_IsSemiring_1570 -> T_IsMonoid_686
d_isMonoid_1634 T_IsSemiring_1570
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))
-- Algebra.Structures.IsSemiring._.isSemigroup
d_isSemigroup_1636 :: T_IsSemiring_1570 -> T_IsSemigroup_472
d_isSemigroup_1636 :: T_IsSemiring_1570 -> T_IsSemigroup_472
d_isSemigroup_1636 T_IsSemiring_1570
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))))
-- Algebra.Structures.IsSemiring._.isUnitalMagma
d_isUnitalMagma_1638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> T_IsUnitalMagma_642
d_isUnitalMagma_1638 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsUnitalMagma_642
d_isUnitalMagma_1638 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsUnitalMagma_642
du_isUnitalMagma_1638 T_IsSemiring_1570
v8
du_isUnitalMagma_1638 :: T_IsSemiring_1570 -> T_IsUnitalMagma_642
du_isUnitalMagma_1638 :: T_IsSemiring_1570 -> T_IsUnitalMagma_642
du_isUnitalMagma_1638 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Structures.IsSemiring._.distrib
d_distrib_1640 ::
  T_IsSemiring_1570 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1640 :: T_IsSemiring_1570 -> T_Σ_14
d_distrib_1640 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.distribʳ
d_distrib'691'_1642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1642 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1642 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1642 T_IsSemiring_1570
v8
du_distrib'691'_1642 ::
  T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1642 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1642 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.distribˡ
d_distrib'737'_1644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1644 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1644 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1644 T_IsSemiring_1570
v8
du_distrib'737'_1644 ::
  T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1644 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1644 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.isEquivalence
d_isEquivalence_1646 ::
  T_IsSemiring_1570 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1646 :: T_IsSemiring_1570 -> T_IsEquivalence_26
d_isEquivalence_1646 T_IsSemiring_1570
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))))))
-- Algebra.Structures.IsSemiring._.isPartialEquivalence
d_isPartialEquivalence_1648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1648 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1648 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1648 T_IsSemiring_1570
v8
du_isPartialEquivalence_1648 ::
  T_IsSemiring_1570 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1648 :: T_IsSemiring_1570 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1648 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Structures.IsSemiring._.refl
d_refl_1650 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_refl_1650 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_refl_1650 T_IsSemiring_1570
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))))))
-- Algebra.Structures.IsSemiring._.reflexive
d_reflexive_1652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1652 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1652 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1652 T_IsSemiring_1570
v8
du_reflexive_1652 ::
  T_IsSemiring_1570 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1652 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1652 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)) AgdaAny
v6)))))
-- Algebra.Structures.IsSemiring._.setoid
d_setoid_1654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1570 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1654 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_Setoid_44
d_setoid_1654 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_Setoid_44
du_setoid_1654 T_IsSemiring_1570
v8
du_setoid_1654 ::
  T_IsSemiring_1570 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1654 :: T_IsSemiring_1570 -> T_Setoid_44
du_setoid_1654 T_IsSemiring_1570
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsSemiring._.sym
d_sym_1656 ::
  T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1656 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1656 T_IsSemiring_1570
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))))))
-- Algebra.Structures.IsSemiring._.trans
d_trans_1658 ::
  T_IsSemiring_1570 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1658 :: T_IsSemiring_1570
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1658 T_IsSemiring_1570
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))))))
-- Algebra.Structures.IsSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_1660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1660 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 T_IsSemiring_1570
v8
du_isSemiringWithoutOne_1660 ::
  T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 :: T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 T_IsSemiring_1570
v0
  = (T_IsCommutativeMonoid_736
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutOne_1298
C_IsSemiringWithoutOne'46'constructor_37629
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0)))
      ((T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_Σ_14
d_zero_1586 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.isNearSemiring
d_isNearSemiring_1664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> T_IsNearSemiring_1218
d_isNearSemiring_1664 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_IsNearSemiring_1218
d_isNearSemiring_1664 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> T_IsNearSemiring_1218
du_isNearSemiring_1664 T_IsSemiring_1570
v8
du_isNearSemiring_1664 ::
  T_IsSemiring_1570 -> T_IsNearSemiring_1218
du_isNearSemiring_1664 :: T_IsSemiring_1570 -> T_IsNearSemiring_1218
du_isNearSemiring_1664 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.zeroʳ
d_zero'691'_1666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_zero'691'_1666 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
d_zero'691'_1666 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_zero'691'_1666 T_IsSemiring_1570
v8
du_zero'691'_1666 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_zero'691'_1666 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_zero'691'_1666 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsSemiring._.zeroˡ
d_zero'737'_1668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1570 -> AgdaAny -> AgdaAny
d_zero'737'_1668 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> AgdaAny
-> AgdaAny
d_zero'737'_1668 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1570
v8
  = T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_zero'737'_1668 T_IsSemiring_1570
v8
du_zero'737'_1668 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_zero'737'_1668 :: T_IsSemiring_1570 -> AgdaAny -> AgdaAny
du_zero'737'_1668 T_IsSemiring_1570
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v0))
-- Algebra.Structures.IsCommutativeSemiring
d_IsCommutativeSemiring_1678 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemiring_1678 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsCommutativeSemiring_1678
  = C_IsCommutativeSemiring'46'constructor_51895 T_IsSemiring_1570
                                                 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemiring.isSemiring
d_isSemiring_1692 ::
  T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 :: T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 T_IsCommutativeSemiring_1678
v0
  = case T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0 of
      C_IsCommutativeSemiring'46'constructor_51895 T_IsSemiring_1570
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1
      T_IsCommutativeSemiring_1678
_ -> T_IsSemiring_1570
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiring.*-comm
d_'42''45'comm_1694 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1694 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1694 T_IsCommutativeSemiring_1678
v0
  = case T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0 of
      C_IsCommutativeSemiring'46'constructor_51895 T_IsSemiring_1570
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemiring_1678
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiring._.*-assoc
d_'42''45'assoc_1698 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1698 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1698 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.*-cong
d_'42''45'cong_1700 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1700 :: T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1700 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1702 T_IsCommutativeSemiring_1678
v8
du_'8729''45'cong'691'_1702 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1702 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1702 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1704 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1704 T_IsCommutativeSemiring_1678
v8
du_'8729''45'cong'737'_1704 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1704 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1704 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsCommutativeSemiring._.*-identity
d_'42''45'identity_1706 ::
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1706 :: T_IsCommutativeSemiring_1678 -> T_Σ_14
d_'42''45'identity_1706 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.identityʳ
d_identity'691'_1708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_identity'691'_1708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
d_identity'691'_1708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'691'_1708 T_IsCommutativeSemiring_1678
v8
du_identity'691'_1708 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'691'_1708 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'691'_1708 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Structures.IsCommutativeSemiring._.identityˡ
d_identity'737'_1710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_identity'737'_1710 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
d_identity'737'_1710 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'737'_1710 T_IsCommutativeSemiring_1678
v8
du_identity'737'_1710 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'737'_1710 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'737'_1710 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Structures.IsCommutativeSemiring._.*-isMagma
d_'42''45'isMagma_1712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeSemiring_1678 -> T_IsMagma_176
d_'42''45'isMagma_1712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsMagma_176
d_'42''45'isMagma_1712 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsMagma_176
du_'42''45'isMagma_1712 T_IsCommutativeSemiring_1678
v8
du_'42''45'isMagma_1712 ::
  T_IsCommutativeSemiring_1678 -> T_IsMagma_176
du_'42''45'isMagma_1712 :: T_IsCommutativeSemiring_1678 -> T_IsMagma_176
du_'42''45'isMagma_1712 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_1714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> T_IsMonoid_686
d_'42''45'isMonoid_1714 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsMonoid_686
d_'42''45'isMonoid_1714 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsMonoid_686
du_'42''45'isMonoid_1714 T_IsCommutativeSemiring_1678
v8
du_'42''45'isMonoid_1714 ::
  T_IsCommutativeSemiring_1678 -> T_IsMonoid_686
du_'42''45'isMonoid_1714 :: T_IsCommutativeSemiring_1678 -> T_IsMonoid_686
du_'42''45'isMonoid_1714 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.*-isSemigroup
d_'42''45'isSemigroup_1716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1716 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1716 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1716 T_IsCommutativeSemiring_1678
v8
du_'42''45'isSemigroup_1716 ::
  T_IsCommutativeSemiring_1678 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1716 :: T_IsCommutativeSemiring_1678 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1716 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.assoc
d_assoc_1718 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1718 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1718 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))))
-- Algebra.Structures.IsCommutativeSemiring._.comm
d_comm_1720 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1720 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1720 T_IsCommutativeSemiring_1678
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-cong
d_'8729''45'cong_1722 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1722 :: T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1722 T_IsCommutativeSemiring_1678
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1724 T_IsCommutativeSemiring_1678
v8
du_'8729''45'cong'691'_1724 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1724 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1724 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1726 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1726 T_IsCommutativeSemiring_1678
v8
du_'8729''45'cong'737'_1726 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1726 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1726 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsCommutativeSemiring._.identity
d_identity_1728 ::
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1728 :: T_IsCommutativeSemiring_1678 -> T_Σ_14
d_identity_1728 T_IsCommutativeSemiring_1678
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))))
-- Algebra.Structures.IsCommutativeSemiring._.identityʳ
d_identity'691'_1730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_identity'691'_1730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
d_identity'691'_1730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'691'_1730 T_IsCommutativeSemiring_1678
v8
du_identity'691'_1730 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'691'_1730 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'691'_1730 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsCommutativeSemiring._.identityˡ
d_identity'737'_1732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_identity'737'_1732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
d_identity'737'_1732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'737'_1732 T_IsCommutativeSemiring_1678
v8
du_identity'737'_1732 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'737'_1732 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_identity'737'_1732 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1734 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1734 T_IsCommutativeSemiring_1678
v8
du_isCommutativeMagma_1734 ::
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1734 :: T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1734 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsCommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1736 ::
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1736 :: T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1736 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_1738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1738 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1738 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1738 T_IsCommutativeSemiring_1678
v8
du_isCommutativeSemigroup_1738 ::
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1738 :: T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1738 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Structures.IsCommutativeSemiring._.isMagma
d_isMagma_1740 :: T_IsCommutativeSemiring_1678 -> T_IsMagma_176
d_isMagma_1740 :: T_IsCommutativeSemiring_1678 -> T_IsMagma_176
d_isMagma_1740 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))))
-- Algebra.Structures.IsCommutativeSemiring._.isMonoid
d_isMonoid_1742 :: T_IsCommutativeSemiring_1678 -> T_IsMonoid_686
d_isMonoid_1742 :: T_IsCommutativeSemiring_1678 -> T_IsMonoid_686
d_isMonoid_1742 T_IsCommutativeSemiring_1678
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))
-- Algebra.Structures.IsCommutativeSemiring._.isSemigroup
d_isSemigroup_1744 ::
  T_IsCommutativeSemiring_1678 -> T_IsSemigroup_472
d_isSemigroup_1744 :: T_IsCommutativeSemiring_1678 -> T_IsSemigroup_472
d_isSemigroup_1744 T_IsCommutativeSemiring_1678
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))))
-- Algebra.Structures.IsCommutativeSemiring._.isUnitalMagma
d_isUnitalMagma_1746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> T_IsUnitalMagma_642
d_isUnitalMagma_1746 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsUnitalMagma_642
d_isUnitalMagma_1746 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsUnitalMagma_642
du_isUnitalMagma_1746 T_IsCommutativeSemiring_1678
v8
du_isUnitalMagma_1746 ::
  T_IsCommutativeSemiring_1678 -> T_IsUnitalMagma_642
du_isUnitalMagma_1746 :: T_IsCommutativeSemiring_1678 -> T_IsUnitalMagma_642
du_isUnitalMagma_1746 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsCommutativeSemiring._.distrib
d_distrib_1748 ::
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1748 :: T_IsCommutativeSemiring_1678 -> T_Σ_14
d_distrib_1748 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.distribʳ
d_distrib'691'_1750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1750 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1750 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1750 T_IsCommutativeSemiring_1678
v8
du_distrib'691'_1750 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1750 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1750 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.distribˡ
d_distrib'737'_1752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1752 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1752 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1752 T_IsCommutativeSemiring_1678
v8
du_distrib'737'_1752 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1752 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1752 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.isEquivalence
d_isEquivalence_1754 ::
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1754 :: T_IsCommutativeSemiring_1678 -> T_IsEquivalence_26
d_isEquivalence_1754 T_IsCommutativeSemiring_1678
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))))))
-- Algebra.Structures.IsCommutativeSemiring._.isNearSemiring
d_isNearSemiring_1756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> T_IsNearSemiring_1218
d_isNearSemiring_1756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsNearSemiring_1218
d_isNearSemiring_1756 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsNearSemiring_1218
du_isNearSemiring_1756 T_IsCommutativeSemiring_1678
v8
du_isNearSemiring_1756 ::
  T_IsCommutativeSemiring_1678 -> T_IsNearSemiring_1218
du_isNearSemiring_1756 :: T_IsCommutativeSemiring_1678 -> T_IsNearSemiring_1218
du_isNearSemiring_1756 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_1758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1758 T_IsCommutativeSemiring_1678
v8
du_isPartialEquivalence_1758 ::
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1758 :: T_IsCommutativeSemiring_1678 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1758 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))))))))
-- Algebra.Structures.IsCommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1760 ::
  T_IsCommutativeSemiring_1678 ->
  T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1760 :: T_IsCommutativeSemiring_1678
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1760 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))
-- Algebra.Structures.IsCommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_1762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1762 T_IsCommutativeSemiring_1678
v8
du_isSemiringWithoutOne_1762 ::
  T_IsCommutativeSemiring_1678 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1762 :: T_IsCommutativeSemiring_1678 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1762 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))
-- Algebra.Structures.IsCommutativeSemiring._.refl
d_refl_1764 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_refl_1764 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_refl_1764 T_IsCommutativeSemiring_1678
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))))))
-- Algebra.Structures.IsCommutativeSemiring._.reflexive
d_reflexive_1766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1766 T_IsCommutativeSemiring_1678
v8
du_reflexive_1766 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1766 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1766 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6)) AgdaAny
v7))))))
-- Algebra.Structures.IsCommutativeSemiring._.setoid
d_setoid_1768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_Setoid_44
d_setoid_1768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_Setoid_44
du_setoid_1768 T_IsCommutativeSemiring_1678
v8
du_setoid_1768 ::
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1768 :: T_IsCommutativeSemiring_1678 -> T_Setoid_44
du_setoid_1768 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsCommutativeSemiring._.sym
d_sym_1770 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1770 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1770 T_IsCommutativeSemiring_1678
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))))))
-- Algebra.Structures.IsCommutativeSemiring._.trans
d_trans_1772 ::
  T_IsCommutativeSemiring_1678 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1772 :: T_IsCommutativeSemiring_1678
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1772 T_IsCommutativeSemiring_1678
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))))))
-- Algebra.Structures.IsCommutativeSemiring._.zero
d_zero_1774 ::
  T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1774 :: T_IsCommutativeSemiring_1678 -> T_Σ_14
d_zero_1774 T_IsCommutativeSemiring_1678
v0 = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1570 -> T_Σ_14
d_zero_1586 ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))
-- Algebra.Structures.IsCommutativeSemiring._.zeroʳ
d_zero'691'_1776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_zero'691'_1776 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
d_zero'691'_1776 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_zero'691'_1776 T_IsCommutativeSemiring_1678
v8
du_zero'691'_1776 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_zero'691'_1776 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_zero'691'_1776 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.zeroˡ
d_zero'737'_1778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
d_zero'737'_1778 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> AgdaAny
-> AgdaAny
d_zero'737'_1778 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_zero'737'_1778 T_IsCommutativeSemiring_1678
v8
du_zero'737'_1778 ::
  T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_zero'737'_1778 :: T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny
du_zero'737'_1778 T_IsCommutativeSemiring_1678
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsCommutativeSemiring.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_1780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 ->
  T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_1780 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_1780 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                       ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 T_IsCommutativeSemiring_1678
v8
du_isCommutativeSemiringWithoutOne_1780 ::
  T_IsCommutativeSemiring_1678 ->
  T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 :: T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 T_IsCommutativeSemiring_1678
v0
  = (T_IsSemiringWithoutOne_1298
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemiringWithoutOne_1382
C_IsCommutativeSemiringWithoutOne'46'constructor_41457
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)))
      ((T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1694 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))
-- Algebra.Structures.IsCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1784 T_IsCommutativeSemiring_1678
v8
du_isCommutativeMagma_1784 ::
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1784 :: T_IsCommutativeSemiring_1678 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1784 T_IsCommutativeSemiring_1678
v0
  = let v1 :: t
v1 = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1786 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                      ~AgdaAny
v7 T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1786 T_IsCommutativeSemiring_1678
v8
du_'42''45'isCommutativeSemigroup_1786 ::
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1786 :: T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1786 T_IsCommutativeSemiring_1678
v0
  = (T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454
      ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))
-- Algebra.Structures.IsCommutativeSemiring.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_1788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_1788 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_1788 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7
                                   T_IsCommutativeSemiring_1678
v8
  = T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1788 T_IsCommutativeSemiring_1678
v8
du_'42''45'isCommutativeMonoid_1788 ::
  T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1788 :: T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1788 T_IsCommutativeSemiring_1678
v0
  = (T_IsMonoid_686
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_736
C_IsCommutativeMonoid'46'constructor_17695
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))))
      ((T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1694 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring
d_IsCancellativeCommutativeSemiring_1798 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCancellativeCommutativeSemiring_1798 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7
  = ()
data T_IsCancellativeCommutativeSemiring_1798
  = C_IsCancellativeCommutativeSemiring'46'constructor_55863 T_IsCommutativeSemiring_1678
                                                             (AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny ->
                                                              (AgdaAny ->
                                                               MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
                                                              AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCancellativeCommutativeSemiring.isCommutativeSemiring
d_isCommutativeSemiring_1812 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 T_IsCancellativeCommutativeSemiring_1798
v0
  = case T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0 of
      C_IsCancellativeCommutativeSemiring'46'constructor_55863 T_IsCommutativeSemiring_1678
v1 AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
v2
        -> T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1
      T_IsCancellativeCommutativeSemiring_1798
_ -> T_IsCommutativeSemiring_1678
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCancellativeCommutativeSemiring.*-cancelˡ-nonZero
d_'42''45'cancel'737''45'nonZero_1814 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  AgdaAny -> AgdaAny
d_'42''45'cancel'737''45'nonZero_1814 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
d_'42''45'cancel'737''45'nonZero_1814 T_IsCancellativeCommutativeSemiring_1798
v0
  = case T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0 of
      C_IsCancellativeCommutativeSemiring'46'constructor_55863 T_IsCommutativeSemiring_1678
v1 AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
v2
        -> (AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> (AgdaAny -> T_Irrelevant_20)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
v2
      T_IsCancellativeCommutativeSemiring_1798
_ -> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-assoc
d_'42''45'assoc_1818 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1818 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1818 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-comm
d_'42''45'comm_1820 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1820 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1820 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1694 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-cong
d_'42''45'cong_1822 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1822 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1822 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1824 T_IsCancellativeCommutativeSemiring_1798
v8
du_'8729''45'cong'691'_1824 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1824 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1824 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1826 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1826 T_IsCancellativeCommutativeSemiring_1798
v8
du_'8729''45'cong'737'_1826 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1826 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1826 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-identity
d_'42''45'identity_1828 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1828 :: T_IsCancellativeCommutativeSemiring_1798 -> T_Σ_14
d_'42''45'identity_1828 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityʳ
d_identity'691'_1830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_identity'691'_1830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
d_identity'691'_1830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'691'_1830 T_IsCancellativeCommutativeSemiring_1798
v8
du_identity'691'_1830 ::
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'691'_1830 :: T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'691'_1830 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityˡ
d_identity'737'_1832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_identity'737'_1832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
d_identity'737'_1832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'737'_1832 T_IsCancellativeCommutativeSemiring_1798
v8
du_identity'737'_1832 ::
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'737'_1832 :: T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'737'_1832 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeMagma_212
d_isCommutativeMagma_1834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1834 T_IsCancellativeCommutativeSemiring_1798
v8
du_isCommutativeMagma_1834 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeMagma_212
du_isCommutativeMagma_1834 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1834 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
            ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_1836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_1836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_1836 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7
                                   T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1836 T_IsCancellativeCommutativeSemiring_1798
v8
du_'42''45'isCommutativeMonoid_1836 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1836 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1836 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1788
      ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                      ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1838 T_IsCancellativeCommutativeSemiring_1798
v8
du_'42''45'isCommutativeSemigroup_1838 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1838 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1838 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454
         ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isMagma
d_'42''45'isMagma_1840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsMagma_176
d_'42''45'isMagma_1840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsMagma_176
d_'42''45'isMagma_1840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> T_IsMagma_176
du_'42''45'isMagma_1840 T_IsCancellativeCommutativeSemiring_1798
v8
du_'42''45'isMagma_1840 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsMagma_176
du_'42''45'isMagma_1840 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsMagma_176
du_'42''45'isMagma_1840 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_1842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsMonoid_686
d_'42''45'isMonoid_1842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsMonoid_686
d_'42''45'isMonoid_1842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> T_IsMonoid_686
du_'42''45'isMonoid_1842 T_IsCancellativeCommutativeSemiring_1798
v8
du_'42''45'isMonoid_1842 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsMonoid_686
du_'42''45'isMonoid_1842 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsMonoid_686
du_'42''45'isMonoid_1842 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isSemigroup
d_'42''45'isSemigroup_1844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1844 T_IsCancellativeCommutativeSemiring_1798
v8
du_'42''45'isSemigroup_1844 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1844 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1844 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.assoc
d_assoc_1846 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1846 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1846 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.comm
d_comm_1848 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1848 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1848 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-cong
d_'8729''45'cong_1850 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1850 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1850 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1852 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1852 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1852 T_IsCancellativeCommutativeSemiring_1798
v8
du_'8729''45'cong'691'_1852 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1852 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1852 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1854 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1854 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1854 T_IsCancellativeCommutativeSemiring_1798
v8
du_'8729''45'cong'737'_1854 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1854 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1854 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identity
d_identity_1856 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1856 :: T_IsCancellativeCommutativeSemiring_1798 -> T_Σ_14
d_identity_1856 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityʳ
d_identity'691'_1858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_identity'691'_1858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
d_identity'691'_1858 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'691'_1858 T_IsCancellativeCommutativeSemiring_1798
v8
du_identity'691'_1858 ::
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'691'_1858 :: T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'691'_1858 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityˡ
d_identity'737'_1860 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_identity'737'_1860 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
d_identity'737'_1860 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'737'_1860 T_IsCancellativeCommutativeSemiring_1798
v8
du_identity'737'_1860 ::
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'737'_1860 :: T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_identity'737'_1860 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeMagma_212
d_isCommutativeMagma_1862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1862 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1862 T_IsCancellativeCommutativeSemiring_1798
v8
du_isCommutativeMagma_1862 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeMagma_212
du_isCommutativeMagma_1862 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1862 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
                  ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1864 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1864 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1864 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_1866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1866 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1866 T_IsCancellativeCommutativeSemiring_1798
v8
du_isCommutativeSemigroup_1866 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1866 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1866 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isMagma
d_isMagma_1868 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsMagma_176
d_isMagma_1868 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsMagma_176
d_isMagma_1868 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isMonoid
d_isMonoid_1870 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsMonoid_686
d_isMonoid_1870 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsMonoid_686
d_isMonoid_1870 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemigroup
d_isSemigroup_1872 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemigroup_472
d_isSemigroup_1872 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemigroup_472
d_isSemigroup_1872 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isUnitalMagma
d_isUnitalMagma_1874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsUnitalMagma_642
d_isUnitalMagma_1874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsUnitalMagma_642
d_isUnitalMagma_1874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> T_IsUnitalMagma_642
du_isUnitalMagma_1874 T_IsCancellativeCommutativeSemiring_1798
v8
du_isUnitalMagma_1874 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsUnitalMagma_642
du_isUnitalMagma_1874 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsUnitalMagma_642
du_isUnitalMagma_1874 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.distrib
d_distrib_1876 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1876 :: T_IsCancellativeCommutativeSemiring_1798 -> T_Σ_14
d_distrib_1876 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.distribʳ
d_distrib'691'_1878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1878 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1878 T_IsCancellativeCommutativeSemiring_1798
v8
du_distrib'691'_1878 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1878 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1878 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.distribˡ
d_distrib'737'_1880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1880 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1880 T_IsCancellativeCommutativeSemiring_1798
v8
du_distrib'737'_1880 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1880 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1880 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_1882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_1882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_1882 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                       ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1882 T_IsCancellativeCommutativeSemiring_1798
v8
du_isCommutativeSemiringWithoutOne_1882 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1882 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1882 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780
      ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isEquivalence
d_isEquivalence_1884 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1884 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsEquivalence_26
d_isEquivalence_1884 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isNearSemiring
d_isNearSemiring_1886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsNearSemiring_1218
d_isNearSemiring_1886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsNearSemiring_1218
d_isNearSemiring_1886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> T_IsNearSemiring_1218
du_isNearSemiring_1886 T_IsCancellativeCommutativeSemiring_1798
v8
du_isNearSemiring_1886 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsNearSemiring_1218
du_isNearSemiring_1886 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsNearSemiring_1218
du_isNearSemiring_1886 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_1888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1888 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1888 T_IsCancellativeCommutativeSemiring_1798
v8
du_isPartialEquivalence_1888 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1888 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1888 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemiring
d_isSemiring_1890 ::
  T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemiring_1570
d_isSemiring_1890 :: T_IsCancellativeCommutativeSemiring_1798 -> T_IsSemiring_1570
d_isSemiring_1890 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1892 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1892 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1892 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_1894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1894 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1894 T_IsCancellativeCommutativeSemiring_1798
v8
du_isSemiringWithoutOne_1894 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1894 :: T_IsCancellativeCommutativeSemiring_1798
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1894 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.refl
d_refl_1896 ::
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_refl_1896 :: T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_refl_1896 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692
                           ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.reflexive
d_reflexive_1898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1898 T_IsCancellativeCommutativeSemiring_1798
v8
du_reflexive_1898 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1898 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1898 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)) AgdaAny
v8)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.setoid
d_setoid_1900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> T_Setoid_44
d_setoid_1900 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> T_Setoid_44
du_setoid_1900 T_IsCancellativeCommutativeSemiring_1798
v8
du_setoid_1900 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1900 :: T_IsCancellativeCommutativeSemiring_1798 -> T_Setoid_44
du_setoid_1900 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.sym
d_sym_1902 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1902 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1902 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692
                           ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.trans
d_trans_1904 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1904 :: T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1904 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692
                           ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.zero
d_zero_1906 ::
  T_IsCancellativeCommutativeSemiring_1798 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1906 :: T_IsCancellativeCommutativeSemiring_1798 -> T_Σ_14
d_zero_1906 T_IsCancellativeCommutativeSemiring_1798
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_Σ_14
d_zero_1586
      ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.zeroʳ
d_zero'691'_1908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_zero'691'_1908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
d_zero'691'_1908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_zero'691'_1908 T_IsCancellativeCommutativeSemiring_1798
v8
du_zero'691'_1908 ::
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_zero'691'_1908 :: T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_zero'691'_1908 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.zeroˡ
d_zero'737'_1910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
d_zero'737'_1910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
d_zero'737'_1910 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_zero'737'_1910 T_IsCancellativeCommutativeSemiring_1798
v8
du_zero'737'_1910 ::
  T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_zero'737'_1910 :: T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny -> AgdaAny
du_zero'737'_1910 T_IsCancellativeCommutativeSemiring_1798
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring.*-cancelʳ-nonZero
d_'42''45'cancel'691''45'nonZero_1912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  AgdaAny -> AgdaAny
d_'42''45'cancel'691''45'nonZero_1912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
d_'42''45'cancel'691''45'nonZero_1912 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                      ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1798
v8
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
du_'42''45'cancel'691''45'nonZero_1912 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsCancellativeCommutativeSemiring_1798
v8
du_'42''45'cancel'691''45'nonZero_1912 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCancellativeCommutativeSemiring_1798 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  AgdaAny -> AgdaAny
du_'42''45'cancel'691''45'nonZero_1912 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
du_'42''45'cancel'691''45'nonZero_1912 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCancellativeCommutativeSemiring_1798
v1
  = (T_Setoid_44
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny
     -> AgdaAny
     -> AgdaAny
     -> (AgdaAny -> T_Irrelevant_20)
     -> AgdaAny
     -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> (AgdaAny -> T_Irrelevant_20)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_44
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny
    -> AgdaAny
    -> AgdaAny
    -> (AgdaAny -> T_Irrelevant_20)
    -> AgdaAny
    -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'8743'almostCancel'737''8658'almostCancel'691'_380
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_1692 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0)
      ((T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1694 ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_1812 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1)))
      ((T_IsCancellativeCommutativeSemiring_1798
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> (AgdaAny -> T_Irrelevant_20)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
d_'42''45'cancel'737''45'nonZero_1814 (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1))
-- Algebra.Structures.IsIdempotentSemiring
d_IsIdempotentSemiring_1922 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentSemiring_1922 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsIdempotentSemiring_1922
  = C_IsIdempotentSemiring'46'constructor_60011 T_IsSemiring_1570
                                                (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentSemiring.isSemiring
d_isSemiring_1936 ::
  T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 :: T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 T_IsIdempotentSemiring_1922
v0
  = case T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0 of
      C_IsIdempotentSemiring'46'constructor_60011 T_IsSemiring_1570
v1 AgdaAny -> AgdaAny
v2 -> T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1
      T_IsIdempotentSemiring_1922
_ -> T_IsSemiring_1570
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentSemiring.+-idem
d_'43''45'idem_1938 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_'43''45'idem_1938 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_'43''45'idem_1938 T_IsIdempotentSemiring_1922
v0
  = case T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0 of
      C_IsIdempotentSemiring'46'constructor_60011 T_IsSemiring_1570
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentSemiring_1922
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentSemiring._.*-assoc
d_'42''45'assoc_1942 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1942 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1942 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))
-- Algebra.Structures.IsIdempotentSemiring._.*-cong
d_'42''45'cong_1944 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1944 :: T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1944 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))
-- Algebra.Structures.IsIdempotentSemiring._.∙-congʳ
d_'8729''45'cong'691'_1946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1946 T_IsIdempotentSemiring_1922
v8
du_'8729''45'cong'691'_1946 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1946 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1946 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsIdempotentSemiring._.∙-congˡ
d_'8729''45'cong'737'_1948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1948 T_IsIdempotentSemiring_1922
v8
du_'8729''45'cong'737'_1948 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1948 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1948 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsIdempotentSemiring._.*-identity
d_'42''45'identity_1950 ::
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1950 :: T_IsIdempotentSemiring_1922 -> T_Σ_14
d_'42''45'identity_1950 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))
-- Algebra.Structures.IsIdempotentSemiring._.identityʳ
d_identity'691'_1952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_identity'691'_1952 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
d_identity'691'_1952 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'691'_1952 T_IsIdempotentSemiring_1922
v8
du_identity'691'_1952 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'691'_1952 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'691'_1952 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Structures.IsIdempotentSemiring._.identityˡ
d_identity'737'_1954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_identity'737'_1954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
d_identity'737'_1954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'737'_1954 T_IsIdempotentSemiring_1922
v8
du_identity'737'_1954 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'737'_1954 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'737'_1954 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Structures.IsIdempotentSemiring._.*-isMagma
d_'42''45'isMagma_1956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsMagma_176
d_'42''45'isMagma_1956 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsMagma_176
d_'42''45'isMagma_1956 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsMagma_176
du_'42''45'isMagma_1956 T_IsIdempotentSemiring_1922
v8
du_'42''45'isMagma_1956 ::
  T_IsIdempotentSemiring_1922 -> T_IsMagma_176
du_'42''45'isMagma_1956 :: T_IsIdempotentSemiring_1922 -> T_IsMagma_176
du_'42''45'isMagma_1956 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.*-isMonoid
d_'42''45'isMonoid_1958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsMonoid_686
d_'42''45'isMonoid_1958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsMonoid_686
d_'42''45'isMonoid_1958 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsMonoid_686
du_'42''45'isMonoid_1958 T_IsIdempotentSemiring_1922
v8
du_'42''45'isMonoid_1958 ::
  T_IsIdempotentSemiring_1922 -> T_IsMonoid_686
du_'42''45'isMonoid_1958 :: T_IsIdempotentSemiring_1922 -> T_IsMonoid_686
du_'42''45'isMonoid_1958 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.*-isSemigroup
d_'42''45'isSemigroup_1960 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1960 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1960 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1960 T_IsIdempotentSemiring_1922
v8
du_'42''45'isSemigroup_1960 ::
  T_IsIdempotentSemiring_1922 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1960 :: T_IsIdempotentSemiring_1922 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1960 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.assoc
d_assoc_1962 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1962 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1962 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))))
-- Algebra.Structures.IsIdempotentSemiring._.comm
d_comm_1964 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1964 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1964 T_IsIdempotentSemiring_1922
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))
-- Algebra.Structures.IsIdempotentSemiring._.∙-cong
d_'8729''45'cong_1966 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1966 :: T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1966 T_IsIdempotentSemiring_1922
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))))))
-- Algebra.Structures.IsIdempotentSemiring._.∙-congʳ
d_'8729''45'cong'691'_1968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1968 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1968 T_IsIdempotentSemiring_1922
v8
du_'8729''45'cong'691'_1968 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1968 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1968 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsIdempotentSemiring._.∙-congˡ
d_'8729''45'cong'737'_1970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1970 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1970 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1970 T_IsIdempotentSemiring_1922
v8
du_'8729''45'cong'737'_1970 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1970 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1970 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsIdempotentSemiring._.identity
d_identity_1972 ::
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1972 :: T_IsIdempotentSemiring_1922 -> T_Σ_14
d_identity_1972 T_IsIdempotentSemiring_1922
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))))
-- Algebra.Structures.IsIdempotentSemiring._.identityʳ
d_identity'691'_1974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_identity'691'_1974 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
d_identity'691'_1974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'691'_1974 T_IsIdempotentSemiring_1922
v8
du_identity'691'_1974 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'691'_1974 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'691'_1974 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsIdempotentSemiring._.identityˡ
d_identity'737'_1976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_identity'737'_1976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
d_identity'737'_1976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'737'_1976 T_IsIdempotentSemiring_1922
v8
du_identity'737'_1976 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'737'_1976 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_identity'737'_1976 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsIdempotentSemiring._.isCommutativeMagma
d_isCommutativeMagma_1978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1978 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1978 T_IsIdempotentSemiring_1922
v8
du_isCommutativeMagma_1978 ::
  T_IsIdempotentSemiring_1922 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1978 :: T_IsIdempotentSemiring_1922 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1978 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsIdempotentSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1980 ::
  T_IsIdempotentSemiring_1922 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1980 :: T_IsIdempotentSemiring_1922 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1980 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))
-- Algebra.Structures.IsIdempotentSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_1982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1982 T_IsIdempotentSemiring_1922
v8
du_isCommutativeSemigroup_1982 ::
  T_IsIdempotentSemiring_1922 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1982 :: T_IsIdempotentSemiring_1922 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1982 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Structures.IsIdempotentSemiring._.isMagma
d_isMagma_1984 :: T_IsIdempotentSemiring_1922 -> T_IsMagma_176
d_isMagma_1984 :: T_IsIdempotentSemiring_1922 -> T_IsMagma_176
d_isMagma_1984 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))))
-- Algebra.Structures.IsIdempotentSemiring._.isMonoid
d_isMonoid_1986 :: T_IsIdempotentSemiring_1922 -> T_IsMonoid_686
d_isMonoid_1986 :: T_IsIdempotentSemiring_1922 -> T_IsMonoid_686
d_isMonoid_1986 T_IsIdempotentSemiring_1922
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))
-- Algebra.Structures.IsIdempotentSemiring._.isSemigroup
d_isSemigroup_1988 ::
  T_IsIdempotentSemiring_1922 -> T_IsSemigroup_472
d_isSemigroup_1988 :: T_IsIdempotentSemiring_1922 -> T_IsSemigroup_472
d_isSemigroup_1988 T_IsIdempotentSemiring_1922
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))))
-- Algebra.Structures.IsIdempotentSemiring._.isUnitalMagma
d_isUnitalMagma_1990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsUnitalMagma_642
d_isUnitalMagma_1990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsUnitalMagma_642
d_isUnitalMagma_1990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsUnitalMagma_642
du_isUnitalMagma_1990 T_IsIdempotentSemiring_1922
v8
du_isUnitalMagma_1990 ::
  T_IsIdempotentSemiring_1922 -> T_IsUnitalMagma_642
du_isUnitalMagma_1990 :: T_IsIdempotentSemiring_1922 -> T_IsUnitalMagma_642
du_isUnitalMagma_1990 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Structures.IsIdempotentSemiring._.distrib
d_distrib_1992 ::
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1992 :: T_IsIdempotentSemiring_1922 -> T_Σ_14
d_distrib_1992 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))
-- Algebra.Structures.IsIdempotentSemiring._.distribʳ
d_distrib'691'_1994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1994 T_IsIdempotentSemiring_1922
v8
du_distrib'691'_1994 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1994 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1994 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.distribˡ
d_distrib'737'_1996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1996 T_IsIdempotentSemiring_1922
v8
du_distrib'737'_1996 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1996 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1996 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.isEquivalence
d_isEquivalence_1998 ::
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1998 :: T_IsIdempotentSemiring_1922 -> T_IsEquivalence_26
d_isEquivalence_1998 T_IsIdempotentSemiring_1922
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0)))))))
-- Algebra.Structures.IsIdempotentSemiring._.isNearSemiring
d_isNearSemiring_2000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsNearSemiring_1218
d_isNearSemiring_2000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsNearSemiring_1218
d_isNearSemiring_2000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsNearSemiring_1218
du_isNearSemiring_2000 T_IsIdempotentSemiring_1922
v8
du_isNearSemiring_2000 ::
  T_IsIdempotentSemiring_1922 -> T_IsNearSemiring_1218
du_isNearSemiring_2000 :: T_IsIdempotentSemiring_1922 -> T_IsNearSemiring_1218
du_isNearSemiring_2000 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.isPartialEquivalence
d_isPartialEquivalence_2002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2002 T_IsIdempotentSemiring_1922
v8
du_isPartialEquivalence_2002 ::
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2002 :: T_IsIdempotentSemiring_1922 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2002 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))))))))
-- Algebra.Structures.IsIdempotentSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2004 ::
  T_IsIdempotentSemiring_1922 ->
  T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2004 :: T_IsIdempotentSemiring_1922
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2004 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))
-- Algebra.Structures.IsIdempotentSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2006 T_IsIdempotentSemiring_1922
v8
du_isSemiringWithoutOne_2006 ::
  T_IsIdempotentSemiring_1922 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2006 :: T_IsIdempotentSemiring_1922 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2006 T_IsIdempotentSemiring_1922
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))
-- Algebra.Structures.IsIdempotentSemiring._.refl
d_refl_2008 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_refl_2008 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_refl_2008 T_IsIdempotentSemiring_1922
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))))))
-- Algebra.Structures.IsIdempotentSemiring._.reflexive
d_reflexive_2010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2010 T_IsIdempotentSemiring_1922
v8
du_reflexive_2010 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2010 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2010 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6)) AgdaAny
v7))))))
-- Algebra.Structures.IsIdempotentSemiring._.setoid
d_setoid_2012 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_Setoid_44
d_setoid_2012 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_Setoid_44
du_setoid_2012 T_IsIdempotentSemiring_1922
v8
du_setoid_2012 ::
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2012 :: T_IsIdempotentSemiring_1922 -> T_Setoid_44
du_setoid_2012 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsIdempotentSemiring._.sym
d_sym_2014 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2014 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2014 T_IsIdempotentSemiring_1922
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))))))
-- Algebra.Structures.IsIdempotentSemiring._.trans
d_trans_2016 ::
  T_IsIdempotentSemiring_1922 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2016 :: T_IsIdempotentSemiring_1922
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2016 T_IsIdempotentSemiring_1922
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))))))
-- Algebra.Structures.IsIdempotentSemiring._.zero
d_zero_2018 ::
  T_IsIdempotentSemiring_1922 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2018 :: T_IsIdempotentSemiring_1922 -> T_Σ_14
d_zero_2018 T_IsIdempotentSemiring_1922
v0 = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1570 -> T_Σ_14
d_zero_1586 ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))
-- Algebra.Structures.IsIdempotentSemiring._.zeroʳ
d_zero'691'_2020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_zero'691'_2020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
d_zero'691'_2020 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_zero'691'_2020 T_IsIdempotentSemiring_1922
v8
du_zero'691'_2020 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_zero'691'_2020 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_zero'691'_2020 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.zeroˡ
d_zero'737'_2022 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_zero'737'_2022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> AgdaAny
-> AgdaAny
d_zero'737'_2022 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_zero'737'_2022 T_IsIdempotentSemiring_1922
v8
du_zero'737'_2022 ::
  T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_zero'737'_2022 :: T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
du_zero'737'_2022 T_IsIdempotentSemiring_1922
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Structures.IsIdempotentSemiring.+-isIdempotentCommutativeMonoid
d_'43''45'isIdempotentCommutativeMonoid_2024 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_2024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_2024 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4
                                             ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 T_IsIdempotentSemiring_1922
v8
du_'43''45'isIdempotentCommutativeMonoid_2024 ::
  T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 :: T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 T_IsIdempotentSemiring_1922
v0
  = (T_IsCommutativeMonoid_736
 -> (AgdaAny -> AgdaAny) -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny -> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736
-> (AgdaAny -> AgdaAny) -> T_IsIdempotentCommutativeMonoid_852
C_IsIdempotentCommutativeMonoid'46'constructor_20685
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))))
      ((T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_'43''45'idem_1938 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))
-- Algebra.Structures.IsIdempotentSemiring._.isBand
d_isBand_2028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsBand_508
d_isBand_2028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsBand_508
d_isBand_2028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsBand_508
du_isBand_2028 T_IsIdempotentSemiring_1922
v8
du_isBand_2028 :: T_IsIdempotentSemiring_1922 -> T_IsBand_508
du_isBand_2028 :: T_IsIdempotentSemiring_1922 -> T_IsBand_508
du_isBand_2028 T_IsIdempotentSemiring_1922
v0
  = let v1 :: t
v1
          = (T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsIdempotentSemiring._.isCommutativeBand
d_isCommutativeBand_2030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsCommutativeBand_590
d_isCommutativeBand_2030 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsCommutativeBand_590
d_isCommutativeBand_2030 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsCommutativeBand_590
du_isCommutativeBand_2030 T_IsIdempotentSemiring_1922
v8
du_isCommutativeBand_2030 ::
  T_IsIdempotentSemiring_1922 -> T_IsCommutativeBand_590
du_isCommutativeBand_2030 :: T_IsIdempotentSemiring_1922 -> T_IsCommutativeBand_590
du_isCommutativeBand_2030 T_IsIdempotentSemiring_1922
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916
      ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))
-- Algebra.Structures.IsIdempotentSemiring._.isIdempotentMonoid
d_isIdempotentMonoid_2032 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsIdempotentSemiring_1922 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2032 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsIdempotentSemiring_1922
v8
  = T_IsIdempotentSemiring_1922 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2032 T_IsIdempotentSemiring_1922
v8
du_isIdempotentMonoid_2032 ::
  T_IsIdempotentSemiring_1922 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2032 :: T_IsIdempotentSemiring_1922 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2032 T_IsIdempotentSemiring_1922
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910
      ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v0))
-- Algebra.Structures.IsKleeneAlgebra
d_IsKleeneAlgebra_2044 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsKleeneAlgebra_2044 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsKleeneAlgebra_2044
  = C_IsKleeneAlgebra'46'constructor_63875 T_IsIdempotentSemiring_1922
                                           MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                           MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsKleeneAlgebra.isIdempotentSemiring
d_isIdempotentSemiring_2062 ::
  T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 :: T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 T_IsKleeneAlgebra_2044
v0
  = case T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0 of
      C_IsKleeneAlgebra'46'constructor_63875 T_IsIdempotentSemiring_1922
v1 T_Σ_14
v2 T_Σ_14
v3 -> T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1
      T_IsKleeneAlgebra_2044
_ -> T_IsIdempotentSemiring_1922
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsKleeneAlgebra.starExpansive
d_starExpansive_2064 ::
  T_IsKleeneAlgebra_2044 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_starExpansive_2064 :: T_IsKleeneAlgebra_2044 -> T_Σ_14
d_starExpansive_2064 T_IsKleeneAlgebra_2044
v0
  = case T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0 of
      C_IsKleeneAlgebra'46'constructor_63875 T_IsIdempotentSemiring_1922
v1 T_Σ_14
v2 T_Σ_14
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsKleeneAlgebra_2044
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsKleeneAlgebra.starDestructive
d_starDestructive_2066 ::
  T_IsKleeneAlgebra_2044 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_starDestructive_2066 :: T_IsKleeneAlgebra_2044 -> T_Σ_14
d_starDestructive_2066 T_IsKleeneAlgebra_2044
v0
  = case T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0 of
      C_IsKleeneAlgebra'46'constructor_63875 T_IsIdempotentSemiring_1922
v1 T_Σ_14
v2 T_Σ_14
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_IsKleeneAlgebra_2044
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsKleeneAlgebra._.*-assoc
d_'42''45'assoc_2070 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2070 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2070 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))
-- Algebra.Structures.IsKleeneAlgebra._.*-cong
d_'42''45'cong_2072 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2072 :: T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2072 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))
-- Algebra.Structures.IsKleeneAlgebra._.∙-congʳ
d_'8729''45'cong'691'_2074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2074 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2074 T_IsKleeneAlgebra_2044
v9
du_'8729''45'cong'691'_2074 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2074 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2074 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsKleeneAlgebra._.∙-congˡ
d_'8729''45'cong'737'_2076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2076 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2076 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2076 T_IsKleeneAlgebra_2044
v9
du_'8729''45'cong'737'_2076 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2076 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2076 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsKleeneAlgebra._.*-identity
d_'42''45'identity_2078 ::
  T_IsKleeneAlgebra_2044 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2078 :: T_IsKleeneAlgebra_2044 -> T_Σ_14
d_'42''45'identity_2078 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))
-- Algebra.Structures.IsKleeneAlgebra._.identityʳ
d_identity'691'_2080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_identity'691'_2080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_identity'691'_2080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'691'_2080 T_IsKleeneAlgebra_2044
v9
du_identity'691'_2080 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'691'_2080 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'691'_2080 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Structures.IsKleeneAlgebra._.identityˡ
d_identity'737'_2082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_identity'737'_2082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_identity'737'_2082 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'737'_2082 T_IsKleeneAlgebra_2044
v9
du_identity'737'_2082 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'737'_2082 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'737'_2082 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Structures.IsKleeneAlgebra._.*-isMagma
d_'42''45'isMagma_2084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsMagma_176
d_'42''45'isMagma_2084 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsMagma_176
d_'42''45'isMagma_2084 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsMagma_176
du_'42''45'isMagma_2084 T_IsKleeneAlgebra_2044
v9
du_'42''45'isMagma_2084 :: T_IsKleeneAlgebra_2044 -> T_IsMagma_176
du_'42''45'isMagma_2084 :: T_IsKleeneAlgebra_2044 -> T_IsMagma_176
du_'42''45'isMagma_2084 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.*-isMonoid
d_'42''45'isMonoid_2086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsMonoid_686
d_'42''45'isMonoid_2086 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsMonoid_686
d_'42''45'isMonoid_2086 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsMonoid_686
du_'42''45'isMonoid_2086 T_IsKleeneAlgebra_2044
v9
du_'42''45'isMonoid_2086 ::
  T_IsKleeneAlgebra_2044 -> T_IsMonoid_686
du_'42''45'isMonoid_2086 :: T_IsKleeneAlgebra_2044 -> T_IsMonoid_686
du_'42''45'isMonoid_2086 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
du_'42''45'isMonoid_1550
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.*-isSemigroup
d_'42''45'isSemigroup_2088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2088 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2088 T_IsKleeneAlgebra_2044
v9
du_'42''45'isSemigroup_2088 ::
  T_IsKleeneAlgebra_2044 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2088 :: T_IsKleeneAlgebra_2044 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2088 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.assoc
d_assoc_2090 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2090 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2090 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))))))
-- Algebra.Structures.IsKleeneAlgebra._.comm
d_comm_2092 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2092 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2092 T_IsKleeneAlgebra_2044
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))))
-- Algebra.Structures.IsKleeneAlgebra._.∙-cong
d_'8729''45'cong_2094 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2094 :: T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2094 T_IsKleeneAlgebra_2044
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))))))
-- Algebra.Structures.IsKleeneAlgebra._.∙-congʳ
d_'8729''45'cong'691'_2096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2096 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2096 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2096 T_IsKleeneAlgebra_2044
v9
du_'8729''45'cong'691'_2096 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2096 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2096 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsKleeneAlgebra._.∙-congˡ
d_'8729''45'cong'737'_2098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2098 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2098 T_IsKleeneAlgebra_2044
v9
du_'8729''45'cong'737'_2098 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2098 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2098 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsKleeneAlgebra._.+-idem
d_'43''45'idem_2100 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_'43''45'idem_2100 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_'43''45'idem_2100 T_IsKleeneAlgebra_2044
v0
  = (T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
d_'43''45'idem_1938 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))
-- Algebra.Structures.IsKleeneAlgebra._.identity
d_identity_2102 ::
  T_IsKleeneAlgebra_2044 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2102 :: T_IsKleeneAlgebra_2044 -> T_Σ_14
d_identity_2102 T_IsKleeneAlgebra_2044
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))))
-- Algebra.Structures.IsKleeneAlgebra._.identityʳ
d_identity'691'_2104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_identity'691'_2104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_identity'691'_2104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'691'_2104 T_IsKleeneAlgebra_2044
v9
du_identity'691'_2104 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'691'_2104 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'691'_2104 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsKleeneAlgebra._.identityˡ
d_identity'737'_2106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_identity'737'_2106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_identity'737'_2106 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'737'_2106 T_IsKleeneAlgebra_2044
v9
du_identity'737'_2106 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'737'_2106 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_identity'737'_2106 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsKleeneAlgebra._.isBand
d_isBand_2108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsBand_508
d_isBand_2108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsBand_508
d_isBand_2108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsBand_508
du_isBand_2108 T_IsKleeneAlgebra_2044
v9
du_isBand_2108 :: T_IsKleeneAlgebra_2044 -> T_IsBand_508
du_isBand_2108 :: T_IsKleeneAlgebra_2044 -> T_IsBand_508
du_isBand_2108 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.isCommutativeBand
d_isCommutativeBand_2110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsCommutativeBand_590
d_isCommutativeBand_2110 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsCommutativeBand_590
d_isCommutativeBand_2110 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsCommutativeBand_590
du_isCommutativeBand_2110 T_IsKleeneAlgebra_2044
v9
du_isCommutativeBand_2110 ::
  T_IsKleeneAlgebra_2044 -> T_IsCommutativeBand_590
du_isCommutativeBand_2110 :: T_IsKleeneAlgebra_2044 -> T_IsCommutativeBand_590
du_isCommutativeBand_2110 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916
         ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1)))
-- Algebra.Structures.IsKleeneAlgebra._.isCommutativeMagma
d_isCommutativeMagma_2112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2112 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2112 T_IsKleeneAlgebra_2044
v9
du_isCommutativeMagma_2112 ::
  T_IsKleeneAlgebra_2044 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2112 :: T_IsKleeneAlgebra_2044 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2112 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
                  ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsKleeneAlgebra._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2114 ::
  T_IsKleeneAlgebra_2044 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2114 :: T_IsKleeneAlgebra_2044 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2114 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))
-- Algebra.Structures.IsKleeneAlgebra._.isCommutativeSemigroup
d_isCommutativeSemigroup_2116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2116 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                              T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2116 T_IsKleeneAlgebra_2044
v9
du_isCommutativeSemigroup_2116 ::
  T_IsKleeneAlgebra_2044 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2116 :: T_IsKleeneAlgebra_2044 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2116 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Structures.IsKleeneAlgebra._.+-isIdempotentCommutativeMonoid
d_'43''45'isIdempotentCommutativeMonoid_2118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 -> T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_2118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_2118 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4
                                             ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2118 T_IsKleeneAlgebra_2044
v9
du_'43''45'isIdempotentCommutativeMonoid_2118 ::
  T_IsKleeneAlgebra_2044 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2118 :: T_IsKleeneAlgebra_2044 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2118 T_IsKleeneAlgebra_2044
v0
  = (T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024
      ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))
-- Algebra.Structures.IsKleeneAlgebra._.isIdempotentMonoid
d_isIdempotentMonoid_2120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2120 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2120 T_IsKleeneAlgebra_2044
v9
du_isIdempotentMonoid_2120 ::
  T_IsKleeneAlgebra_2044 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2120 :: T_IsKleeneAlgebra_2044 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2120 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910
         ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2024 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1)))
-- Algebra.Structures.IsKleeneAlgebra._.isMagma
d_isMagma_2122 :: T_IsKleeneAlgebra_2044 -> T_IsMagma_176
d_isMagma_2122 :: T_IsKleeneAlgebra_2044 -> T_IsMagma_176
d_isMagma_2122 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))))))
-- Algebra.Structures.IsKleeneAlgebra._.isMonoid
d_isMonoid_2124 :: T_IsKleeneAlgebra_2044 -> T_IsMonoid_686
d_isMonoid_2124 :: T_IsKleeneAlgebra_2044 -> T_IsMonoid_686
d_isMonoid_2124 T_IsKleeneAlgebra_2044
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))))
-- Algebra.Structures.IsKleeneAlgebra._.isSemigroup
d_isSemigroup_2126 :: T_IsKleeneAlgebra_2044 -> T_IsSemigroup_472
d_isSemigroup_2126 :: T_IsKleeneAlgebra_2044 -> T_IsSemigroup_472
d_isSemigroup_2126 T_IsKleeneAlgebra_2044
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))))
-- Algebra.Structures.IsKleeneAlgebra._.isUnitalMagma
d_isUnitalMagma_2128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsUnitalMagma_642
d_isUnitalMagma_2128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsUnitalMagma_642
d_isUnitalMagma_2128 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsUnitalMagma_642
du_isUnitalMagma_2128 T_IsKleeneAlgebra_2044
v9
du_isUnitalMagma_2128 ::
  T_IsKleeneAlgebra_2044 -> T_IsUnitalMagma_642
du_isUnitalMagma_2128 :: T_IsKleeneAlgebra_2044 -> T_IsUnitalMagma_642
du_isUnitalMagma_2128 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Structures.IsKleeneAlgebra._.distrib
d_distrib_2130 ::
  T_IsKleeneAlgebra_2044 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2130 :: T_IsKleeneAlgebra_2044 -> T_Σ_14
d_distrib_2130 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))
-- Algebra.Structures.IsKleeneAlgebra._.distribʳ
d_distrib'691'_2132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2132 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2132 T_IsKleeneAlgebra_2044
v9
du_distrib'691'_2132 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2132 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2132 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.distribˡ
d_distrib'737'_2134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2134 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2134 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2134 T_IsKleeneAlgebra_2044
v9
du_distrib'737'_2134 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2134 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2134 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.isEquivalence
d_isEquivalence_2136 ::
  T_IsKleeneAlgebra_2044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2136 :: T_IsKleeneAlgebra_2044 -> T_IsEquivalence_26
d_isEquivalence_2136 T_IsKleeneAlgebra_2044
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))))))))
-- Algebra.Structures.IsKleeneAlgebra._.isNearSemiring
d_isNearSemiring_2138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsNearSemiring_1218
d_isNearSemiring_2138 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsNearSemiring_1218
d_isNearSemiring_2138 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsNearSemiring_1218
du_isNearSemiring_2138 T_IsKleeneAlgebra_2044
v9
du_isNearSemiring_2138 ::
  T_IsKleeneAlgebra_2044 -> T_IsNearSemiring_1218
du_isNearSemiring_2138 :: T_IsKleeneAlgebra_2044 -> T_IsNearSemiring_1218
du_isNearSemiring_2138 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.isPartialEquivalence
d_isPartialEquivalence_2140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2140 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2140 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2140 T_IsKleeneAlgebra_2044
v9
du_isPartialEquivalence_2140 ::
  T_IsKleeneAlgebra_2044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2140 :: T_IsKleeneAlgebra_2044 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2140 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)))))))))
-- Algebra.Structures.IsKleeneAlgebra._.isSemiring
d_isSemiring_2142 :: T_IsKleeneAlgebra_2044 -> T_IsSemiring_1570
d_isSemiring_2142 :: T_IsKleeneAlgebra_2044 -> T_IsSemiring_1570
d_isSemiring_2142 T_IsKleeneAlgebra_2044
v0
  = (T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))
-- Algebra.Structures.IsKleeneAlgebra._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2144 ::
  T_IsKleeneAlgebra_2044 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2144 :: T_IsKleeneAlgebra_2044 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2144 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))
-- Algebra.Structures.IsKleeneAlgebra._.isSemiringWithoutOne
d_isSemiringWithoutOne_2146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsKleeneAlgebra_2044 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2146 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2146 T_IsKleeneAlgebra_2044
v9
du_isSemiringWithoutOne_2146 ::
  T_IsKleeneAlgebra_2044 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2146 :: T_IsKleeneAlgebra_2044 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2146 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1)))
-- Algebra.Structures.IsKleeneAlgebra._.refl
d_refl_2148 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_refl_2148 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_refl_2148 T_IsKleeneAlgebra_2044
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))))))))
-- Algebra.Structures.IsKleeneAlgebra._.reflexive
d_reflexive_2150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2150 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2150 T_IsKleeneAlgebra_2044
v9
du_reflexive_2150 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2150 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2150 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)) AgdaAny
v8)))))))
-- Algebra.Structures.IsKleeneAlgebra._.setoid
d_setoid_2152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2152 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> T_Setoid_44
d_setoid_2152 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> T_Setoid_44
du_setoid_2152 T_IsKleeneAlgebra_2044
v9
du_setoid_2152 ::
  T_IsKleeneAlgebra_2044 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2152 :: T_IsKleeneAlgebra_2044 -> T_Setoid_44
du_setoid_2152 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3 = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsKleeneAlgebra._.sym
d_sym_2154 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2154 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2154 T_IsKleeneAlgebra_2044
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))))))))
-- Algebra.Structures.IsKleeneAlgebra._.trans
d_trans_2156 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2156 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2156 T_IsKleeneAlgebra_2044
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))))))))
-- Algebra.Structures.IsKleeneAlgebra._.zero
d_zero_2158 ::
  T_IsKleeneAlgebra_2044 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2158 :: T_IsKleeneAlgebra_2044 -> T_Σ_14
d_zero_2158 T_IsKleeneAlgebra_2044
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_Σ_14
d_zero_1586
      ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0)))
-- Algebra.Structures.IsKleeneAlgebra._.zeroʳ
d_zero'691'_2160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_zero'691'_2160 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_zero'691'_2160 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_zero'691'_2160 T_IsKleeneAlgebra_2044
v9
du_zero'691'_2160 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_zero'691'_2160 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_zero'691'_2160 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra._.zeroˡ
d_zero'737'_2162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_zero'737'_2162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_zero'737'_2162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_zero'737'_2162 T_IsKleeneAlgebra_2044
v9
du_zero'737'_2162 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_zero'737'_2162 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_zero'737'_2162 T_IsKleeneAlgebra_2044
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2062 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2 = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Structures.IsKleeneAlgebra.starExpansiveˡ
d_starExpansive'737'_2164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_starExpansive'737'_2164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_starExpansive'737'_2164 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_starExpansive'737'_2164 T_IsKleeneAlgebra_2044
v9
du_starExpansive'737'_2164 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_starExpansive'737'_2164 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_starExpansive'737'_2164 T_IsKleeneAlgebra_2044
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_IsKleeneAlgebra_2044 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_Σ_14
d_starExpansive_2064 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))
-- Algebra.Structures.IsKleeneAlgebra.starExpansiveʳ
d_starExpansive'691'_2166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
d_starExpansive'691'_2166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
d_starExpansive'691'_2166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_starExpansive'691'_2166 T_IsKleeneAlgebra_2044
v9
du_starExpansive'691'_2166 ::
  T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_starExpansive'691'_2166 :: T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
du_starExpansive'691'_2166 T_IsKleeneAlgebra_2044
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_IsKleeneAlgebra_2044 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_Σ_14
d_starExpansive_2064 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))
-- Algebra.Structures.IsKleeneAlgebra.starDestructiveˡ
d_starDestructive'737'_2168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_starDestructive'737'_2168 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_starDestructive'737'_2168 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'737'_2168 T_IsKleeneAlgebra_2044
v9
du_starDestructive'737'_2168 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'737'_2168 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'737'_2168 T_IsKleeneAlgebra_2044
v0
  = (T_Σ_14 -> AgdaAny)
-> 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_IsKleeneAlgebra_2044 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_Σ_14
d_starDestructive_2066 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))
-- Algebra.Structures.IsKleeneAlgebra.starDestructiveʳ
d_starDestructive'691'_2170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_starDestructive'691'_2170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsKleeneAlgebra_2044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_starDestructive'691'_2170 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsKleeneAlgebra_2044
v9
  = T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'691'_2170 T_IsKleeneAlgebra_2044
v9
du_starDestructive'691'_2170 ::
  T_IsKleeneAlgebra_2044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'691'_2170 :: T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'691'_2170 T_IsKleeneAlgebra_2044
v0
  = (T_Σ_14 -> AgdaAny)
-> 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_IsKleeneAlgebra_2044 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044 -> T_Σ_14
d_starDestructive_2066 (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v0))
-- Algebra.Structures.IsQuasiring
d_IsQuasiring_2180 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasiring_2180 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsQuasiring_2180
  = C_IsQuasiring'46'constructor_69993 T_IsMonoid_686
                                       (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
                                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsQuasiring.+-isMonoid
d_'43''45'isMonoid_2202 :: T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 :: T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 T_IsQuasiring_2180
v0
  = case T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0 of
      C_IsQuasiring'46'constructor_69993 T_IsMonoid_686
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
v6 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsQuasiring_2180
_ -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasiring.*-cong
d_'42''45'cong_2204 ::
  T_IsQuasiring_2180 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2204 :: T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2204 T_IsQuasiring_2180
v0
  = case T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0 of
      C_IsQuasiring'46'constructor_69993 T_IsMonoid_686
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
v6 -> (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_IsQuasiring_2180
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasiring.*-assoc
d_'42''45'assoc_2206 ::
  T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2206 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2206 T_IsQuasiring_2180
v0
  = case T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0 of
      C_IsQuasiring'46'constructor_69993 T_IsMonoid_686
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
v6 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsQuasiring_2180
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasiring.*-identity
d_'42''45'identity_2208 ::
  T_IsQuasiring_2180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2208 :: T_IsQuasiring_2180 -> T_Σ_14
d_'42''45'identity_2208 T_IsQuasiring_2180
v0
  = case T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0 of
      C_IsQuasiring'46'constructor_69993 T_IsMonoid_686
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
v6 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsQuasiring_2180
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasiring.distrib
d_distrib_2210 ::
  T_IsQuasiring_2180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2210 :: T_IsQuasiring_2180 -> T_Σ_14
d_distrib_2210 T_IsQuasiring_2180
v0
  = case T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0 of
      C_IsQuasiring'46'constructor_69993 T_IsMonoid_686
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
v6 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v5
      T_IsQuasiring_2180
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasiring.zero
d_zero_2212 ::
  T_IsQuasiring_2180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2212 :: T_IsQuasiring_2180 -> T_Σ_14
d_zero_2212 T_IsQuasiring_2180
v0
  = case T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0 of
      C_IsQuasiring'46'constructor_69993 T_IsMonoid_686
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
v6 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v6
      T_IsQuasiring_2180
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasiring._.assoc
d_assoc_2216 ::
  T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2216 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2216 T_IsQuasiring_2180
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0)))
-- Algebra.Structures.IsQuasiring._.∙-cong
d_'8729''45'cong_2218 ::
  T_IsQuasiring_2180 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2218 :: T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2218 T_IsQuasiring_2180
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))))
-- Algebra.Structures.IsQuasiring._.∙-congʳ
d_'8729''45'cong'691'_2220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2220 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2220 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2220 T_IsQuasiring_2180
v8
du_'8729''45'cong'691'_2220 ::
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2220 :: T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2220 T_IsQuasiring_2180
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsQuasiring._.∙-congˡ
d_'8729''45'cong'737'_2222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2222 T_IsQuasiring_2180
v8
du_'8729''45'cong'737'_2222 ::
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2222 :: T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2222 T_IsQuasiring_2180
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsQuasiring._.identity
d_identity_2224 ::
  T_IsQuasiring_2180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2224 :: T_IsQuasiring_2180 -> T_Σ_14
d_identity_2224 T_IsQuasiring_2180
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring._.identityʳ
d_identity'691'_2226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_identity'691'_2226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_identity'691'_2226 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2226 T_IsQuasiring_2180
v8
du_identity'691'_2226 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2226 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2226 T_IsQuasiring_2180
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring._.identityˡ
d_identity'737'_2228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_identity'737'_2228 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_identity'737'_2228 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2228 T_IsQuasiring_2180
v8
du_identity'737'_2228 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2228 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2228 T_IsQuasiring_2180
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring._.isMagma
d_isMagma_2230 :: T_IsQuasiring_2180 -> T_IsMagma_176
d_isMagma_2230 :: T_IsQuasiring_2180 -> T_IsMagma_176
d_isMagma_2230 T_IsQuasiring_2180
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0)))
-- Algebra.Structures.IsQuasiring._.isSemigroup
d_isSemigroup_2232 :: T_IsQuasiring_2180 -> T_IsSemigroup_472
d_isSemigroup_2232 :: T_IsQuasiring_2180 -> T_IsSemigroup_472
d_isSemigroup_2232 T_IsQuasiring_2180
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring._.isUnitalMagma
d_isUnitalMagma_2234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> T_IsUnitalMagma_642
d_isUnitalMagma_2234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_IsUnitalMagma_642
d_isUnitalMagma_2234 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> T_IsUnitalMagma_642
du_isUnitalMagma_2234 T_IsQuasiring_2180
v8
du_isUnitalMagma_2234 :: T_IsQuasiring_2180 -> T_IsUnitalMagma_642
du_isUnitalMagma_2234 :: T_IsQuasiring_2180 -> T_IsUnitalMagma_642
du_isUnitalMagma_2234 T_IsQuasiring_2180
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring._.isEquivalence
d_isEquivalence_2236 ::
  T_IsQuasiring_2180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2236 :: T_IsQuasiring_2180 -> T_IsEquivalence_26
d_isEquivalence_2236 T_IsQuasiring_2180
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))))
-- Algebra.Structures.IsQuasiring._.isPartialEquivalence
d_isPartialEquivalence_2238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2238 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2238 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2238 T_IsQuasiring_2180
v8
du_isPartialEquivalence_2238 ::
  T_IsQuasiring_2180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2238 :: T_IsQuasiring_2180 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2238 T_IsQuasiring_2180
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsQuasiring._.refl
d_refl_2240 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_refl_2240 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_refl_2240 T_IsQuasiring_2180
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0)))))
-- Algebra.Structures.IsQuasiring._.reflexive
d_reflexive_2242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2242 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2242 T_IsQuasiring_2180
v8
du_reflexive_2242 ::
  T_IsQuasiring_2180 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2242 :: T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2242 T_IsQuasiring_2180
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsQuasiring._.setoid
d_setoid_2244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_Setoid_44
d_setoid_2244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> T_Setoid_44
du_setoid_2244 T_IsQuasiring_2180
v8
du_setoid_2244 ::
  T_IsQuasiring_2180 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2244 :: T_IsQuasiring_2180 -> T_Setoid_44
du_setoid_2244 T_IsQuasiring_2180
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsQuasiring._.sym
d_sym_2246 ::
  T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2246 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2246 T_IsQuasiring_2180
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0)))))
-- Algebra.Structures.IsQuasiring._.trans
d_trans_2248 ::
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2248 :: T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2248 T_IsQuasiring_2180
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0)))))
-- Algebra.Structures.IsQuasiring.distribˡ
d_distrib'737'_2250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2250 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2250 T_IsQuasiring_2180
v8
du_distrib'737'_2250 ::
  T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2250 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2250 T_IsQuasiring_2180
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_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_distrib_2210 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.distribʳ
d_distrib'691'_2252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2252 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2252 T_IsQuasiring_2180
v8
du_distrib'691'_2252 ::
  T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2252 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2252 T_IsQuasiring_2180
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_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_distrib_2210 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.zeroˡ
d_zero'737'_2254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_zero'737'_2254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_zero'737'_2254 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'737'_2254 T_IsQuasiring_2180
v8
du_zero'737'_2254 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'737'_2254 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'737'_2254 T_IsQuasiring_2180
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_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_zero_2212 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.zeroʳ
d_zero'691'_2256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_zero'691'_2256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_zero'691'_2256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'691'_2256 T_IsQuasiring_2180
v8
du_zero'691'_2256 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'691'_2256 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'691'_2256 T_IsQuasiring_2180
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_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_zero_2212 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.identityˡ
d_identity'737'_2258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_identity'737'_2258 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_identity'737'_2258 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2258 T_IsQuasiring_2180
v8
du_identity'737'_2258 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2258 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2258 T_IsQuasiring_2180
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_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_'42''45'identity_2208 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.identityʳ
d_identity'691'_2260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_identity'691'_2260 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_identity'691'_2260 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2260 T_IsQuasiring_2180
v8
du_identity'691'_2260 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2260 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2260 T_IsQuasiring_2180
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_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_'42''45'identity_2208 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.*-isMagma
d_'42''45'isMagma_2262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> T_IsMagma_176
d_'42''45'isMagma_2262 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_IsMagma_176
d_'42''45'isMagma_2262 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> T_IsMagma_176
du_'42''45'isMagma_2262 T_IsQuasiring_2180
v8
du_'42''45'isMagma_2262 :: T_IsQuasiring_2180 -> T_IsMagma_176
du_'42''45'isMagma_2262 :: T_IsQuasiring_2180 -> T_IsMagma_176
du_'42''45'isMagma_2262 T_IsQuasiring_2180
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0)))))
      ((T_IsQuasiring_2180
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2204 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.*-isSemigroup
d_'42''45'isSemigroup_2264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2264 T_IsQuasiring_2180
v8
du_'42''45'isSemigroup_2264 ::
  T_IsQuasiring_2180 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2264 :: T_IsQuasiring_2180 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2264 T_IsQuasiring_2180
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
C_IsSemigroup'46'constructor_10417
      ((T_IsQuasiring_2180 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMagma_176
du_'42''45'isMagma_2262 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
      ((T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2206 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring.*-isMonoid
d_'42''45'isMonoid_2266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> T_IsMonoid_686
d_'42''45'isMonoid_2266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_IsMonoid_686
d_'42''45'isMonoid_2266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 T_IsQuasiring_2180
v8
du_'42''45'isMonoid_2266 :: T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 :: T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 T_IsQuasiring_2180
v0
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
C_IsMonoid'46'constructor_15873
      ((T_IsQuasiring_2180 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2264 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
      ((T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_'42''45'identity_2208 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring._.∙-congʳ
d_'8729''45'cong'691'_2270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2270 T_IsQuasiring_2180
v8
du_'8729''45'cong'691'_2270 ::
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2270 :: T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2270 T_IsQuasiring_2180
v0
  = let v1 :: t
v1 = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsQuasiring._.∙-congˡ
d_'8729''45'cong'737'_2272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2272 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2272 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2272 T_IsQuasiring_2180
v8
du_'8729''45'cong'737'_2272 ::
  T_IsQuasiring_2180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2272 :: T_IsQuasiring_2180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2272 T_IsQuasiring_2180
v0
  = let v1 :: t
v1 = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsQuasiring._.identityʳ
d_identity'691'_2274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_identity'691'_2274 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_identity'691'_2274 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2274 T_IsQuasiring_2180
v8
du_identity'691'_2274 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2274 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2274 T_IsQuasiring_2180
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsQuasiring._.identityˡ
d_identity'737'_2276 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
d_identity'737'_2276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
d_identity'737'_2276 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsQuasiring_2180
v8
  = T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2276 T_IsQuasiring_2180
v8
du_identity'737'_2276 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2276 :: T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2276 T_IsQuasiring_2180
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v0))
-- Algebra.Structures.IsRingWithoutOne
d_IsRingWithoutOne_2286 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOne_2286 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsRingWithoutOne_2286
  = C_IsRingWithoutOne'46'constructor_75855 T_IsAbelianGroup_1132
                                            (AgdaAny ->
                                             AgdaAny ->
                                             AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                            MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsRingWithoutOne.+-isAbelianGroup
d_'43''45'isAbelianGroup_2304 ::
  T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 :: T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 T_IsRingWithoutOne_2286
v0
  = case T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0 of
      C_IsRingWithoutOne'46'constructor_75855 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 -> T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1
      T_IsRingWithoutOne_2286
_ -> T_IsAbelianGroup_1132
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRingWithoutOne.*-cong
d_'42''45'cong_2306 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2306 :: T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2306 T_IsRingWithoutOne_2286
v0
  = case T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0 of
      C_IsRingWithoutOne'46'constructor_75855 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 -> (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_IsRingWithoutOne_2286
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRingWithoutOne.*-assoc
d_'42''45'assoc_2308 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2308 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2308 T_IsRingWithoutOne_2286
v0
  = case T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0 of
      C_IsRingWithoutOne'46'constructor_75855 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsRingWithoutOne_2286
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRingWithoutOne.distrib
d_distrib_2310 ::
  T_IsRingWithoutOne_2286 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2310 :: T_IsRingWithoutOne_2286 -> T_Σ_14
d_distrib_2310 T_IsRingWithoutOne_2286
v0
  = case T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0 of
      C_IsRingWithoutOne'46'constructor_75855 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsRingWithoutOne_2286
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRingWithoutOne._._//_
d__'47''47'__2314 ::
  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 -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__2314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__2314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~T_IsRingWithoutOne_2286
v8
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2314 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'47''47'__2314 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2314 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2314 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsRingWithoutOne._.assoc
d_assoc_2316 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2316 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2316 T_IsRingWithoutOne_2286
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))))
-- Algebra.Structures.IsRingWithoutOne._.comm
d_comm_2318 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2318 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2318 T_IsRingWithoutOne_2286
v0
  = (T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
-- Algebra.Structures.IsRingWithoutOne._.∙-cong
d_'8729''45'cong_2320 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2320 :: T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2320 T_IsRingWithoutOne_2286
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))))))
-- Algebra.Structures.IsRingWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_2322 ::
  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 ->
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2322 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2322 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2322 T_IsRingWithoutOne_2286
v8
du_'8729''45'cong'691'_2322 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2322 :: T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2322 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsRingWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_2324 ::
  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 ->
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2324 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2324 T_IsRingWithoutOne_2286
v8
du_'8729''45'cong'737'_2324 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2324 :: T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2324 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsRingWithoutOne._.identity
d_identity_2326 ::
  T_IsRingWithoutOne_2286 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2326 :: T_IsRingWithoutOne_2286 -> T_Σ_14
d_identity_2326 T_IsRingWithoutOne_2286
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))))
-- Algebra.Structures.IsRingWithoutOne._.identityʳ
d_identity'691'_2328 ::
  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 -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_identity'691'_2328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
d_identity'691'_2328 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_identity'691'_2328 T_IsRingWithoutOne_2286
v8
du_identity'691'_2328 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_identity'691'_2328 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_identity'691'_2328 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Structures.IsRingWithoutOne._.identityˡ
d_identity'737'_2330 ::
  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 -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_identity'737'_2330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
d_identity'737'_2330 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_identity'737'_2330 T_IsRingWithoutOne_2286
v8
du_identity'737'_2330 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_identity'737'_2330 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_identity'737'_2330 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Structures.IsRingWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_2332 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2332 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2332 T_IsRingWithoutOne_2286
v8
du_isCommutativeMagma_2332 ::
  T_IsRingWithoutOne_2286 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2332 :: T_IsRingWithoutOne_2286 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2332 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsRingWithoutOne._.isCommutativeMonoid
d_isCommutativeMonoid_2334 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2334 T_IsRingWithoutOne_2286
v8
du_isCommutativeMonoid_2334 ::
  T_IsRingWithoutOne_2286 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2334 :: T_IsRingWithoutOne_2286 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2334 T_IsRingWithoutOne_2286
v0
  = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204
      ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
-- Algebra.Structures.IsRingWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_2336 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2336 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2336 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2336 T_IsRingWithoutOne_2286
v8
du_isCommutativeSemigroup_2336 ::
  T_IsRingWithoutOne_2286 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2336 :: T_IsRingWithoutOne_2286 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2336 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
         ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsRingWithoutOne._.isGroup
d_isGroup_2338 :: T_IsRingWithoutOne_2286 -> T_IsGroup_1036
d_isGroup_2338 :: T_IsRingWithoutOne_2286 -> T_IsGroup_1036
d_isGroup_2338 T_IsRingWithoutOne_2286
v0
  = (T_IsAbelianGroup_1132 -> T_IsGroup_1036)
-> AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
-- Algebra.Structures.IsRingWithoutOne._.isInvertibleMagma
d_isInvertibleMagma_2340 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_2340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_2340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2340 T_IsRingWithoutOne_2286
v8
du_isInvertibleMagma_2340 ::
  T_IsRingWithoutOne_2286 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2340 :: T_IsRingWithoutOne_2286 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2340 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsRingWithoutOne._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_2342 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2342 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2342 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2342 T_IsRingWithoutOne_2286
v8
du_isInvertibleUnitalMagma_2342 ::
  T_IsRingWithoutOne_2286 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2342 :: T_IsRingWithoutOne_2286 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2342 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsRingWithoutOne._.isMagma
d_isMagma_2344 :: T_IsRingWithoutOne_2286 -> T_IsMagma_176
d_isMagma_2344 :: T_IsRingWithoutOne_2286 -> T_IsMagma_176
d_isMagma_2344 T_IsRingWithoutOne_2286
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))))
-- Algebra.Structures.IsRingWithoutOne._.isMonoid
d_isMonoid_2346 :: T_IsRingWithoutOne_2286 -> T_IsMonoid_686
d_isMonoid_2346 :: T_IsRingWithoutOne_2286 -> T_IsMonoid_686
d_isMonoid_2346 T_IsRingWithoutOne_2286
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))
-- Algebra.Structures.IsRingWithoutOne._.isSemigroup
d_isSemigroup_2348 :: T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
d_isSemigroup_2348 :: T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
d_isSemigroup_2348 T_IsRingWithoutOne_2286
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))))
-- Algebra.Structures.IsRingWithoutOne._.isUnitalMagma
d_isUnitalMagma_2350 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsUnitalMagma_642
d_isUnitalMagma_2350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsUnitalMagma_642
d_isUnitalMagma_2350 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsUnitalMagma_642
du_isUnitalMagma_2350 T_IsRingWithoutOne_2286
v8
du_isUnitalMagma_2350 ::
  T_IsRingWithoutOne_2286 -> T_IsUnitalMagma_642
du_isUnitalMagma_2350 :: T_IsRingWithoutOne_2286 -> T_IsUnitalMagma_642
du_isUnitalMagma_2350 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Structures.IsRingWithoutOne._.⁻¹-cong
d_'8315''185''45'cong_2352 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2352 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2352 T_IsRingWithoutOne_2286
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))
-- Algebra.Structures.IsRingWithoutOne._.inverse
d_inverse_2354 ::
  T_IsRingWithoutOne_2286 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2354 :: T_IsRingWithoutOne_2286 -> T_Σ_14
d_inverse_2354 T_IsRingWithoutOne_2286
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_Σ_14
d_inverse_1052
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))
-- Algebra.Structures.IsRingWithoutOne._.inverseʳ
d_inverse'691'_2356 ::
  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 -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_inverse'691'_2356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
d_inverse'691'_2356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_inverse'691'_2356 T_IsRingWithoutOne_2286
v8
du_inverse'691'_2356 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_inverse'691'_2356 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_inverse'691'_2356 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsRingWithoutOne._.inverseˡ
d_inverse'737'_2358 ::
  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 -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_inverse'737'_2358 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
d_inverse'737'_2358 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_inverse'737'_2358 T_IsRingWithoutOne_2286
v8
du_inverse'737'_2358 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_inverse'737'_2358 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_inverse'737'_2358 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsRingWithoutOne._.isEquivalence
d_isEquivalence_2360 ::
  T_IsRingWithoutOne_2286 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2360 :: T_IsRingWithoutOne_2286 -> T_IsEquivalence_26
d_isEquivalence_2360 T_IsRingWithoutOne_2286
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))))))
-- Algebra.Structures.IsRingWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_2362 ::
  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 ->
  T_IsRingWithoutOne_2286 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2362 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2362 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2362 T_IsRingWithoutOne_2286
v8
du_isPartialEquivalence_2362 ::
  T_IsRingWithoutOne_2286 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2362 :: T_IsRingWithoutOne_2286 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2362 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Structures.IsRingWithoutOne._.refl
d_refl_2364 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_refl_2364 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_refl_2364 T_IsRingWithoutOne_2286
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))))))
-- Algebra.Structures.IsRingWithoutOne._.reflexive
d_reflexive_2366 ::
  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 ->
  T_IsRingWithoutOne_2286 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2366 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2366 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2366 T_IsRingWithoutOne_2286
v8
du_reflexive_2366 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2366 :: T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2366 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)) AgdaAny
v6)))))
-- Algebra.Structures.IsRingWithoutOne._.setoid
d_setoid_2368 ::
  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 ->
  T_IsRingWithoutOne_2286 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2368 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Setoid_44
d_setoid_2368 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_Setoid_44
du_setoid_2368 T_IsRingWithoutOne_2286
v8
du_setoid_2368 ::
  T_IsRingWithoutOne_2286 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2368 :: T_IsRingWithoutOne_2286 -> T_Setoid_44
du_setoid_2368 T_IsRingWithoutOne_2286
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsRingWithoutOne._.sym
d_sym_2370 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2370 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2370 T_IsRingWithoutOne_2286
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))))))
-- Algebra.Structures.IsRingWithoutOne._.trans
d_trans_2372 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2372 :: T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2372 T_IsRingWithoutOne_2286
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))))))
-- Algebra.Structures.IsRingWithoutOne._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2374 ::
  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 ->
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_2374 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_2374 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2374 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
du_unique'691''45''8315''185'_2374 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2374 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2374 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsRingWithoutOne_2286
v3
  = let v4 :: T_IsAbelianGroup_1132
v4 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4)))
-- Algebra.Structures.IsRingWithoutOne._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2376 ::
  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 ->
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_2376 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_2376 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2376 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
du_unique'737''45''8315''185'_2376 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2376 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2376 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsRingWithoutOne_2286
v3
  = let v4 :: T_IsAbelianGroup_1132
v4 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4)))
-- Algebra.Structures.IsRingWithoutOne.distribˡ
d_distrib'737'_2378 ::
  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 ->
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2378 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2378 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2378 T_IsRingWithoutOne_2286
v8
du_distrib'737'_2378 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2378 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2378 T_IsRingWithoutOne_2286
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_IsRingWithoutOne_2286 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_Σ_14
d_distrib_2310 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
-- Algebra.Structures.IsRingWithoutOne.distribʳ
d_distrib'691'_2380 ::
  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 ->
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2380 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2380 T_IsRingWithoutOne_2286
v8
du_distrib'691'_2380 ::
  T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2380 :: T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2380 T_IsRingWithoutOne_2286
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_IsRingWithoutOne_2286 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_Σ_14
d_distrib_2310 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
-- Algebra.Structures.IsRingWithoutOne.zeroˡ
d_zero'737'_2382 ::
  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 -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_zero'737'_2382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
d_zero'737'_2382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'737'_2382 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
du_zero'737'_2382 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_zero'737'_2382 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'737'_2382 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRingWithoutOne_2286
v4
  = (T_Setoid_44
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_44
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_assoc'8743'distrib'691''8743'id'691''8743'inv'691''8658'ze'737'_594
      (let v5 :: T_IsGroup_1036
v5
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v6 :: T_IsMonoid_686
v6 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v5) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v7 :: T_IsSemigroup_472
v7 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7))))))
      ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4)))))))
      ((T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2306 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))))))
      ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2380 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))
      (let v5 :: T_IsGroup_1036
v5
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v5))))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))))
-- Algebra.Structures.IsRingWithoutOne.zeroʳ
d_zero'691'_2384 ::
  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 -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
d_zero'691'_2384 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
d_zero'691'_2384 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'691'_2384 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
du_zero'691'_2384 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny
du_zero'691'_2384 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'691'_2384 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRingWithoutOne_2286
v4
  = (T_Setoid_44
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_44
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_assoc'8743'distrib'737''8743'id'691''8743'inv'691''8658'ze'691'_606
      (let v5 :: T_IsGroup_1036
v5
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v6 :: T_IsMonoid_686
v6 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v5) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v7 :: T_IsSemigroup_472
v7 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7))))))
      ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4)))))))
      ((T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2306 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))))))
      ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2378 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))
      (let v5 :: T_IsGroup_1036
v5
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v5))))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))))
-- Algebra.Structures.IsRingWithoutOne.zero
d_zero_2386 ::
  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 ->
  T_IsRingWithoutOne_2286 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2386 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
d_zero_2386 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
du_zero_2386 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRingWithoutOne_2286
v8
du_zero_2386 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRingWithoutOne_2286 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_2386 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
du_zero_2386 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRingWithoutOne_2286
v4
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'737'_2382 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'691'_2384 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4))
-- Algebra.Structures.IsRingWithoutOne.*-isMagma
d_'42''45'isMagma_2388 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsMagma_176
d_'42''45'isMagma_2388 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsMagma_176
d_'42''45'isMagma_2388 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsMagma_176
du_'42''45'isMagma_2388 T_IsRingWithoutOne_2286
v8
du_'42''45'isMagma_2388 :: T_IsRingWithoutOne_2286 -> T_IsMagma_176
du_'42''45'isMagma_2388 :: T_IsRingWithoutOne_2286 -> T_IsMagma_176
du_'42''45'isMagma_2388 T_IsRingWithoutOne_2286
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0)))))))
      ((T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2306 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
-- Algebra.Structures.IsRingWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_2390 ::
  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 -> T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 T_IsRingWithoutOne_2286
v8
du_'42''45'isSemigroup_2390 ::
  T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 :: T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 T_IsRingWithoutOne_2286
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
C_IsSemigroup'46'constructor_10417
      ((T_IsRingWithoutOne_2286 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsMagma_176
du_'42''45'isMagma_2388 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
      ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2308 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0))
-- Algebra.Structures.IsRingWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_2394 ::
  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 ->
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2394 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2394 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2394 T_IsRingWithoutOne_2286
v8
du_'8729''45'cong'691'_2394 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2394 :: T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2394 T_IsRingWithoutOne_2286
v0
  = let v1 :: t
v1 = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsRingWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_2396 ::
  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 ->
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRingWithoutOne_2286
v8
  = T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2396 T_IsRingWithoutOne_2286
v8
du_'8729''45'cong'737'_2396 ::
  T_IsRingWithoutOne_2286 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2396 :: T_IsRingWithoutOne_2286
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2396 T_IsRingWithoutOne_2286
v0
  = let v1 :: t
v1 = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsNonAssociativeRing
d_IsNonAssociativeRing_2408 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNonAssociativeRing_2408 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsNonAssociativeRing_2408
  = C_IsNonAssociativeRing'46'constructor_83447 T_IsAbelianGroup_1132
                                                (AgdaAny ->
                                                 AgdaAny ->
                                                 AgdaAny ->
                                                 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsNonAssociativeRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_2430 ::
  T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 :: T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 T_IsNonAssociativeRing_2408
v0
  = case T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0 of
      C_IsNonAssociativeRing'46'constructor_83447 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1
      T_IsNonAssociativeRing_2408
_ -> T_IsAbelianGroup_1132
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNonAssociativeRing.*-cong
d_'42''45'cong_2432 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2432 :: T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2432 T_IsNonAssociativeRing_2408
v0
  = case T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0 of
      C_IsNonAssociativeRing'46'constructor_83447 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
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_IsNonAssociativeRing_2408
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNonAssociativeRing.*-identity
d_'42''45'identity_2434 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2434 :: T_IsNonAssociativeRing_2408 -> T_Σ_14
d_'42''45'identity_2434 T_IsNonAssociativeRing_2408
v0
  = case T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0 of
      C_IsNonAssociativeRing'46'constructor_83447 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_IsNonAssociativeRing_2408
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNonAssociativeRing.distrib
d_distrib_2436 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2436 :: T_IsNonAssociativeRing_2408 -> T_Σ_14
d_distrib_2436 T_IsNonAssociativeRing_2408
v0
  = case T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0 of
      C_IsNonAssociativeRing'46'constructor_83447 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
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_IsNonAssociativeRing_2408
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNonAssociativeRing.zero
d_zero_2438 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2438 :: T_IsNonAssociativeRing_2408 -> T_Σ_14
d_zero_2438 T_IsNonAssociativeRing_2408
v0
  = case T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0 of
      C_IsNonAssociativeRing'46'constructor_83447 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
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_IsNonAssociativeRing_2408
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNonAssociativeRing._._//_
d__'47''47'__2442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__2442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__2442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 ~T_IsNonAssociativeRing_2408
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2442 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'47''47'__2442 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2442 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2442 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsNonAssociativeRing._.assoc
d_assoc_2444 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2444 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2444 T_IsNonAssociativeRing_2408
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))))
-- Algebra.Structures.IsNonAssociativeRing._.comm
d_comm_2446 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2446 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2446 T_IsNonAssociativeRing_2408
v0
  = (T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing._.∙-cong
d_'8729''45'cong_2448 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2448 :: T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2448 T_IsNonAssociativeRing_2408
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))))))
-- Algebra.Structures.IsNonAssociativeRing._.∙-congʳ
d_'8729''45'cong'691'_2450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2450 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2450 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2450 T_IsNonAssociativeRing_2408
v9
du_'8729''45'cong'691'_2450 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2450 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2450 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsNonAssociativeRing._.∙-congˡ
d_'8729''45'cong'737'_2452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2452 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2452 T_IsNonAssociativeRing_2408
v9
du_'8729''45'cong'737'_2452 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2452 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2452 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsNonAssociativeRing._.identity
d_identity_2454 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2454 :: T_IsNonAssociativeRing_2408 -> T_Σ_14
d_identity_2454 T_IsNonAssociativeRing_2408
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))))
-- Algebra.Structures.IsNonAssociativeRing._.identityʳ
d_identity'691'_2456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_identity'691'_2456 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_identity'691'_2456 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_identity'691'_2456 T_IsNonAssociativeRing_2408
v9
du_identity'691'_2456 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_identity'691'_2456 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_identity'691'_2456 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Structures.IsNonAssociativeRing._.identityˡ
d_identity'737'_2458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_identity'737'_2458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_identity'737'_2458 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_identity'737'_2458 T_IsNonAssociativeRing_2408
v9
du_identity'737'_2458 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_identity'737'_2458 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_identity'737'_2458 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Structures.IsNonAssociativeRing._.isCommutativeMagma
d_isCommutativeMagma_2460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2460 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2460 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2460 T_IsNonAssociativeRing_2408
v9
du_isCommutativeMagma_2460 ::
  T_IsNonAssociativeRing_2408 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2460 :: T_IsNonAssociativeRing_2408 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2460 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsNonAssociativeRing._.isCommutativeMonoid
d_isCommutativeMonoid_2462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2462 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2462 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2462 T_IsNonAssociativeRing_2408
v9
du_isCommutativeMonoid_2462 ::
  T_IsNonAssociativeRing_2408 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2462 :: T_IsNonAssociativeRing_2408 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2462 T_IsNonAssociativeRing_2408
v0
  = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204
      ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_2464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2464 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2464 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                              T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2464 T_IsNonAssociativeRing_2408
v9
du_isCommutativeSemigroup_2464 ::
  T_IsNonAssociativeRing_2408 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2464 :: T_IsNonAssociativeRing_2408 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2464 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
         ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsNonAssociativeRing._.isGroup
d_isGroup_2466 :: T_IsNonAssociativeRing_2408 -> T_IsGroup_1036
d_isGroup_2466 :: T_IsNonAssociativeRing_2408 -> T_IsGroup_1036
d_isGroup_2466 T_IsNonAssociativeRing_2408
v0
  = (T_IsAbelianGroup_1132 -> T_IsGroup_1036)
-> AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing._.isInvertibleMagma
d_isInvertibleMagma_2468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_2468 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_2468 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2468 T_IsNonAssociativeRing_2408
v9
du_isInvertibleMagma_2468 ::
  T_IsNonAssociativeRing_2408 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2468 :: T_IsNonAssociativeRing_2408 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2468 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsNonAssociativeRing._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_2470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2470 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2470 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                               T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2470 T_IsNonAssociativeRing_2408
v9
du_isInvertibleUnitalMagma_2470 ::
  T_IsNonAssociativeRing_2408 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2470 :: T_IsNonAssociativeRing_2408 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2470 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsNonAssociativeRing._.isMagma
d_isMagma_2472 :: T_IsNonAssociativeRing_2408 -> T_IsMagma_176
d_isMagma_2472 :: T_IsNonAssociativeRing_2408 -> T_IsMagma_176
d_isMagma_2472 T_IsNonAssociativeRing_2408
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))))
-- Algebra.Structures.IsNonAssociativeRing._.isMonoid
d_isMonoid_2474 :: T_IsNonAssociativeRing_2408 -> T_IsMonoid_686
d_isMonoid_2474 :: T_IsNonAssociativeRing_2408 -> T_IsMonoid_686
d_isMonoid_2474 T_IsNonAssociativeRing_2408
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))
-- Algebra.Structures.IsNonAssociativeRing._.isSemigroup
d_isSemigroup_2476 ::
  T_IsNonAssociativeRing_2408 -> T_IsSemigroup_472
d_isSemigroup_2476 :: T_IsNonAssociativeRing_2408 -> T_IsSemigroup_472
d_isSemigroup_2476 T_IsNonAssociativeRing_2408
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))))
-- Algebra.Structures.IsNonAssociativeRing._.isUnitalMagma
d_isUnitalMagma_2478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
d_isUnitalMagma_2478 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsUnitalMagma_642
d_isUnitalMagma_2478 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_isUnitalMagma_2478 T_IsNonAssociativeRing_2408
v9
du_isUnitalMagma_2478 ::
  T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_isUnitalMagma_2478 :: T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_isUnitalMagma_2478 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Structures.IsNonAssociativeRing._.⁻¹-cong
d_'8315''185''45'cong_2480 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2480 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2480 T_IsNonAssociativeRing_2408
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))
-- Algebra.Structures.IsNonAssociativeRing._.inverse
d_inverse_2482 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2482 :: T_IsNonAssociativeRing_2408 -> T_Σ_14
d_inverse_2482 T_IsNonAssociativeRing_2408
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_Σ_14
d_inverse_1052
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))
-- Algebra.Structures.IsNonAssociativeRing._.inverseʳ
d_inverse'691'_2484 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_inverse'691'_2484 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_inverse'691'_2484 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_inverse'691'_2484 T_IsNonAssociativeRing_2408
v9
du_inverse'691'_2484 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_inverse'691'_2484 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_inverse'691'_2484 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsNonAssociativeRing._.inverseˡ
d_inverse'737'_2486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_inverse'737'_2486 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_inverse'737'_2486 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_inverse'737'_2486 T_IsNonAssociativeRing_2408
v9
du_inverse'737'_2486 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_inverse'737'_2486 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_inverse'737'_2486 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Structures.IsNonAssociativeRing._.isEquivalence
d_isEquivalence_2488 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2488 :: T_IsNonAssociativeRing_2408 -> T_IsEquivalence_26
d_isEquivalence_2488 T_IsNonAssociativeRing_2408
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))))))
-- Algebra.Structures.IsNonAssociativeRing._.isPartialEquivalence
d_isPartialEquivalence_2490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2490 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2490 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2490 T_IsNonAssociativeRing_2408
v9
du_isPartialEquivalence_2490 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2490 :: T_IsNonAssociativeRing_2408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2490 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Structures.IsNonAssociativeRing._.refl
d_refl_2492 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_refl_2492 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_refl_2492 T_IsNonAssociativeRing_2408
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))))))
-- Algebra.Structures.IsNonAssociativeRing._.reflexive
d_reflexive_2494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2494 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2494 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2494 T_IsNonAssociativeRing_2408
v9
du_reflexive_2494 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2494 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2494 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)) AgdaAny
v6)))))
-- Algebra.Structures.IsNonAssociativeRing._.setoid
d_setoid_2496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2496 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_Setoid_44
d_setoid_2496 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_Setoid_44
du_setoid_2496 T_IsNonAssociativeRing_2408
v9
du_setoid_2496 ::
  T_IsNonAssociativeRing_2408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2496 :: T_IsNonAssociativeRing_2408 -> T_Setoid_44
du_setoid_2496 T_IsNonAssociativeRing_2408
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsNonAssociativeRing._.sym
d_sym_2498 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2498 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2498 T_IsNonAssociativeRing_2408
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))))))
-- Algebra.Structures.IsNonAssociativeRing._.trans
d_trans_2500 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2500 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2500 T_IsNonAssociativeRing_2408
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))))))
-- Algebra.Structures.IsNonAssociativeRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_2502 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_2502 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsNonAssociativeRing_2408
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2502 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v9
du_unique'691''45''8315''185'_2502 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2502 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2502 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsNonAssociativeRing_2408
v3
  = let v4 :: T_IsAbelianGroup_1132
v4 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4)))
-- Algebra.Structures.IsNonAssociativeRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_2504 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_2504 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsNonAssociativeRing_2408
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2504 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v9
du_unique'737''45''8315''185'_2504 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2504 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2504 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsNonAssociativeRing_2408
v3
  = let v4 :: T_IsAbelianGroup_1132
v4 = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4)))
-- Algebra.Structures.IsNonAssociativeRing.zeroˡ
d_zero'737'_2506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_zero'737'_2506 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_zero'737'_2506 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_zero'737'_2506 T_IsNonAssociativeRing_2408
v9
du_zero'737'_2506 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_zero'737'_2506 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_zero'737'_2506 T_IsNonAssociativeRing_2408
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_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_Σ_14
d_zero_2438 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing.zeroʳ
d_zero'691'_2508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_zero'691'_2508 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_zero'691'_2508 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_zero'691'_2508 T_IsNonAssociativeRing_2408
v9
du_zero'691'_2508 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_zero'691'_2508 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_zero'691'_2508 T_IsNonAssociativeRing_2408
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_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_Σ_14
d_zero_2438 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing.distribˡ
d_distrib'737'_2510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2510 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2510 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2510 T_IsNonAssociativeRing_2408
v9
du_distrib'737'_2510 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2510 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2510 T_IsNonAssociativeRing_2408
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_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_Σ_14
d_distrib_2436 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing.distribʳ
d_distrib'691'_2512 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2512 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2512 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2512 T_IsNonAssociativeRing_2408
v9
du_distrib'691'_2512 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2512 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2512 T_IsNonAssociativeRing_2408
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_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_Σ_14
d_distrib_2436 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing.*-isMagma
d_'42''45'isMagma_2514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsNonAssociativeRing_2408 -> T_IsMagma_176
d_'42''45'isMagma_2514 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsMagma_176
d_'42''45'isMagma_2514 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsMagma_176
du_'42''45'isMagma_2514 T_IsNonAssociativeRing_2408
v9
du_'42''45'isMagma_2514 ::
  T_IsNonAssociativeRing_2408 -> T_IsMagma_176
du_'42''45'isMagma_2514 :: T_IsNonAssociativeRing_2408 -> T_IsMagma_176
du_'42''45'isMagma_2514 T_IsNonAssociativeRing_2408
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2430 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0)))))))
      ((T_IsNonAssociativeRing_2408
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2432 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing.*-identityˡ
d_'42''45'identity'737'_2516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_'42''45'identity'737'_2516 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_'42''45'identity'737'_2516 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_'42''45'identity'737'_2516 T_IsNonAssociativeRing_2408
v9
du_'42''45'identity'737'_2516 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_'42''45'identity'737'_2516 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_'42''45'identity'737'_2516 T_IsNonAssociativeRing_2408
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_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_Σ_14
d_'42''45'identity_2434 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing.*-identityʳ
d_'42''45'identity'691'_2518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
d_'42''45'identity'691'_2518 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
d_'42''45'identity'691'_2518 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_'42''45'identity'691'_2518 T_IsNonAssociativeRing_2408
v9
du_'42''45'identity'691'_2518 ::
  T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_'42''45'identity'691'_2518 :: T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
du_'42''45'identity'691'_2518 T_IsNonAssociativeRing_2408
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_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_Σ_14
d_'42''45'identity_2434 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing.*-isUnitalMagma
d_'42''45'isUnitalMagma_2520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
d_'42''45'isUnitalMagma_2520 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> T_IsUnitalMagma_642
d_'42''45'isUnitalMagma_2520 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_2520 T_IsNonAssociativeRing_2408
v9
du_'42''45'isUnitalMagma_2520 ::
  T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_2520 :: T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_2520 T_IsNonAssociativeRing_2408
v0
  = (T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642)
-> AgdaAny -> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642
C_IsUnitalMagma'46'constructor_14317
      ((T_IsNonAssociativeRing_2408 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsMagma_176
du_'42''45'isMagma_2514 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
      ((T_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_Σ_14
d_'42''45'identity_2434 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0))
-- Algebra.Structures.IsNonAssociativeRing._.∙-congʳ
d_'8729''45'cong'691'_2524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2524 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2524 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2524 T_IsNonAssociativeRing_2408
v9
du_'8729''45'cong'691'_2524 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2524 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2524 T_IsNonAssociativeRing_2408
v0
  = let v1 :: t
v1 = (T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_2520 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsNonAssociativeRing._.∙-congˡ
d_'8729''45'cong'737'_2526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2526 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2526 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsNonAssociativeRing_2408
v9
  = T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2526 T_IsNonAssociativeRing_2408
v9
du_'8729''45'cong'737'_2526 ::
  T_IsNonAssociativeRing_2408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2526 :: T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2526 T_IsNonAssociativeRing_2408
v0
  = let v1 :: t
v1 = (T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_2520 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsNearring
d_IsNearring_2538 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearring_2538 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsNearring_2538
  = C_IsNearring'46'constructor_90609 T_IsQuasiring_2180
                                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsNearring.isQuasiring
d_isQuasiring_2556 :: T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 :: T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 T_IsNearring_2538
v0
  = case T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0 of
      C_IsNearring'46'constructor_90609 T_IsQuasiring_2180
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1
      T_IsNearring_2538
_ -> T_IsQuasiring_2180
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearring.+-inverse
d_'43''45'inverse_2558 ::
  T_IsNearring_2538 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'inverse_2558 :: T_IsNearring_2538 -> T_Σ_14
d_'43''45'inverse_2558 T_IsNearring_2538
v0
  = case T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0 of
      C_IsNearring'46'constructor_90609 T_IsQuasiring_2180
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_IsNearring_2538
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearring.⁻¹-cong
d_'8315''185''45'cong_2560 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2560 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2560 T_IsNearring_2538
v0
  = case T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0 of
      C_IsNearring'46'constructor_90609 T_IsQuasiring_2180
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_IsNearring_2538
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearring._.*-assoc
d_'42''45'assoc_2564 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2564 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2564 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2206 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.*-cong
d_'42''45'cong_2566 ::
  T_IsNearring_2538 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2566 :: T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2566 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2204 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.∙-congʳ
d_'8729''45'cong'691'_2568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2568 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2568 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2568 T_IsNearring_2538
v9
du_'8729''45'cong'691'_2568 ::
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2568 :: T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2568 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsNearring._.∙-congˡ
d_'8729''45'cong'737'_2570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2570 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2570 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2570 T_IsNearring_2538
v9
du_'8729''45'cong'737'_2570 ::
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2570 :: T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2570 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsNearring._.*-identity
d_'42''45'identity_2572 ::
  T_IsNearring_2538 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2572 :: T_IsNearring_2538 -> T_Σ_14
d_'42''45'identity_2572 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_'42''45'identity_2208 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.identityʳ
d_identity'691'_2574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_identity'691'_2574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_identity'691'_2574 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2574 T_IsNearring_2538
v9
du_identity'691'_2574 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2574 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2574 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Structures.IsNearring._.identityˡ
d_identity'737'_2576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_identity'737'_2576 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_identity'737'_2576 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2576 T_IsNearring_2538
v9
du_identity'737'_2576 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2576 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2576 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Structures.IsNearring._.*-isMagma
d_'42''45'isMagma_2578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> T_IsMagma_176
d_'42''45'isMagma_2578 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> T_IsMagma_176
d_'42''45'isMagma_2578 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> T_IsMagma_176
du_'42''45'isMagma_2578 T_IsNearring_2538
v9
du_'42''45'isMagma_2578 :: T_IsNearring_2538 -> T_IsMagma_176
du_'42''45'isMagma_2578 :: T_IsNearring_2538 -> T_IsMagma_176
du_'42''45'isMagma_2578 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMagma_176
du_'42''45'isMagma_2262 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.*-isMonoid
d_'42''45'isMonoid_2580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> T_IsMonoid_686
d_'42''45'isMonoid_2580 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> T_IsMonoid_686
d_'42''45'isMonoid_2580 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> T_IsMonoid_686
du_'42''45'isMonoid_2580 T_IsNearring_2538
v9
du_'42''45'isMonoid_2580 :: T_IsNearring_2538 -> T_IsMonoid_686
du_'42''45'isMonoid_2580 :: T_IsNearring_2538 -> T_IsMonoid_686
du_'42''45'isMonoid_2580 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
du_'42''45'isMonoid_2266 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.*-isSemigroup
d_'42''45'isSemigroup_2582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2582 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2582 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2582 T_IsNearring_2538
v9
du_'42''45'isSemigroup_2582 ::
  T_IsNearring_2538 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2582 :: T_IsNearring_2538 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2582 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2264 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.assoc
d_assoc_2584 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2584 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2584 T_IsNearring_2538
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))))
-- Algebra.Structures.IsNearring._.∙-cong
d_'8729''45'cong_2586 ::
  T_IsNearring_2538 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2586 :: T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2586 T_IsNearring_2538
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0)))))
-- Algebra.Structures.IsNearring._.∙-congʳ
d_'8729''45'cong'691'_2588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2588 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2588 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2588 T_IsNearring_2538
v9
du_'8729''45'cong'691'_2588 ::
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2588 :: T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2588 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsNearring._.∙-congˡ
d_'8729''45'cong'737'_2590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2590 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2590 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2590 T_IsNearring_2538
v9
du_'8729''45'cong'737'_2590 ::
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2590 :: T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2590 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsNearring._.identity
d_identity_2592 ::
  T_IsNearring_2538 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2592 :: T_IsNearring_2538 -> T_Σ_14
d_identity_2592 T_IsNearring_2538
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0)))
-- Algebra.Structures.IsNearring._.identityʳ
d_identity'691'_2594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_identity'691'_2594 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_identity'691'_2594 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2594 T_IsNearring_2538
v9
du_identity'691'_2594 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2594 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2594 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Structures.IsNearring._.identityˡ
d_identity'737'_2596 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_identity'737'_2596 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_identity'737'_2596 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2596 T_IsNearring_2538
v9
du_identity'737'_2596 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2596 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2596 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Structures.IsNearring._.isMagma
d_isMagma_2598 :: T_IsNearring_2538 -> T_IsMagma_176
d_isMagma_2598 :: T_IsNearring_2538 -> T_IsMagma_176
d_isMagma_2598 T_IsNearring_2538
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))))
-- Algebra.Structures.IsNearring._.+-isMonoid
d_'43''45'isMonoid_2600 :: T_IsNearring_2538 -> T_IsMonoid_686
d_'43''45'isMonoid_2600 :: T_IsNearring_2538 -> T_IsMonoid_686
d_'43''45'isMonoid_2600 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.isSemigroup
d_isSemigroup_2602 :: T_IsNearring_2538 -> T_IsSemigroup_472
d_isSemigroup_2602 :: T_IsNearring_2538 -> T_IsSemigroup_472
d_isSemigroup_2602 T_IsNearring_2538
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0)))
-- Algebra.Structures.IsNearring._.isUnitalMagma
d_isUnitalMagma_2604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> T_IsUnitalMagma_642
d_isUnitalMagma_2604 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> T_IsUnitalMagma_642
d_isUnitalMagma_2604 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> T_IsUnitalMagma_642
du_isUnitalMagma_2604 T_IsNearring_2538
v9
du_isUnitalMagma_2604 :: T_IsNearring_2538 -> T_IsUnitalMagma_642
du_isUnitalMagma_2604 :: T_IsNearring_2538 -> T_IsUnitalMagma_642
du_isUnitalMagma_2604 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Structures.IsNearring._.distrib
d_distrib_2606 ::
  T_IsNearring_2538 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2606 :: T_IsNearring_2538 -> T_Σ_14
d_distrib_2606 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_distrib_2210 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.distribʳ
d_distrib'691'_2608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2608 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2608 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2608 T_IsNearring_2538
v9
du_distrib'691'_2608 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2608 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2608 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2252 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.distribˡ
d_distrib'737'_2610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2610 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2610 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2610 T_IsNearring_2538
v9
du_distrib'737'_2610 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2610 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2610 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2250 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.identityʳ
d_identity'691'_2612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_identity'691'_2612 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_identity'691'_2612 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2612 T_IsNearring_2538
v9
du_identity'691'_2612 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2612 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'691'_2612 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'691'_2260 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.identityˡ
d_identity'737'_2614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_identity'737'_2614 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_identity'737'_2614 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2614 T_IsNearring_2538
v9
du_identity'737'_2614 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2614 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_identity'737'_2614 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_identity'737'_2258 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.isEquivalence
d_isEquivalence_2616 ::
  T_IsNearring_2538 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2616 :: T_IsNearring_2538 -> T_IsEquivalence_26
d_isEquivalence_2616 T_IsNearring_2538
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0)))))
-- Algebra.Structures.IsNearring._.isPartialEquivalence
d_isPartialEquivalence_2618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2618 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2618 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2618 T_IsNearring_2538
v9
du_isPartialEquivalence_2618 ::
  T_IsNearring_2538 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2618 :: T_IsNearring_2538 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2618 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsNearring._.refl
d_refl_2620 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_refl_2620 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_refl_2620 T_IsNearring_2538
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))))))
-- Algebra.Structures.IsNearring._.reflexive
d_reflexive_2622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2622 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2622 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2622 T_IsNearring_2538
v9
du_reflexive_2622 ::
  T_IsNearring_2538 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2622 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2622 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsNearring._.setoid
d_setoid_2624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearring_2538 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2624 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> T_Setoid_44
d_setoid_2624 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> T_Setoid_44
du_setoid_2624 T_IsNearring_2538
v9
du_setoid_2624 ::
  T_IsNearring_2538 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2624 :: T_IsNearring_2538 -> T_Setoid_44
du_setoid_2624 T_IsNearring_2538
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsNearring._.sym
d_sym_2626 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2626 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2626 T_IsNearring_2538
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))))))
-- Algebra.Structures.IsNearring._.trans
d_trans_2628 ::
  T_IsNearring_2538 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2628 :: T_IsNearring_2538
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2628 T_IsNearring_2538
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_IsMonoid_686
d_'43''45'isMonoid_2202 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))))))
-- Algebra.Structures.IsNearring._.zero
d_zero_2630 ::
  T_IsNearring_2538 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2630 :: T_IsNearring_2538 -> T_Σ_14
d_zero_2630 T_IsNearring_2538
v0 = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsQuasiring_2180 -> T_Σ_14
d_zero_2212 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.zeroʳ
d_zero'691'_2632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_zero'691'_2632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_zero'691'_2632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_zero'691'_2632 T_IsNearring_2538
v9
du_zero'691'_2632 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_zero'691'_2632 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_zero'691'_2632 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'691'_2256 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring._.zeroˡ
d_zero'737'_2634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_zero'737'_2634 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_zero'737'_2634 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_zero'737'_2634 T_IsNearring_2538
v9
du_zero'737'_2634 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_zero'737'_2634 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_zero'737'_2634 T_IsNearring_2538
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
du_zero'737'_2254 ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring.+-inverseˡ
d_'43''45'inverse'737'_2636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_'43''45'inverse'737'_2636 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_'43''45'inverse'737'_2636 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_'43''45'inverse'737'_2636 T_IsNearring_2538
v9
du_'43''45'inverse'737'_2636 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_'43''45'inverse'737'_2636 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_'43''45'inverse'737'_2636 T_IsNearring_2538
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_IsNearring_2538 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_Σ_14
d_'43''45'inverse_2558 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsNearring.+-inverseʳ
d_'43''45'inverse'691'_2638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsNearring_2538 -> AgdaAny -> AgdaAny
d_'43''45'inverse'691'_2638 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsNearring_2538
-> AgdaAny
-> AgdaAny
d_'43''45'inverse'691'_2638 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 T_IsNearring_2538
v9
  = T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_'43''45'inverse'691'_2638 T_IsNearring_2538
v9
du_'43''45'inverse'691'_2638 ::
  T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_'43''45'inverse'691'_2638 :: T_IsNearring_2538 -> AgdaAny -> AgdaAny
du_'43''45'inverse'691'_2638 T_IsNearring_2538
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_IsNearring_2538 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_Σ_14
d_'43''45'inverse_2558 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v0))
-- Algebra.Structures.IsRing
d_IsRing_2650 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRing_2650 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsRing_2650
  = C_IsRing'46'constructor_95033 T_IsAbelianGroup_1132
                                  (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.IsRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_2672 ::
  T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 :: T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 T_IsRing_2650
v0
  = case T_IsRing_2650 -> T_IsRing_2650
forall a b. a -> b
coe T_IsRing_2650
v0 of
      C_IsRing'46'constructor_95033 T_IsAbelianGroup_1132
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5 -> T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1
      T_IsRing_2650
_ -> T_IsAbelianGroup_1132
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.*-cong
d_'42''45'cong_2674 ::
  T_IsRing_2650 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2674 :: T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2674 T_IsRing_2650
v0
  = case T_IsRing_2650 -> T_IsRing_2650
forall a b. a -> b
coe T_IsRing_2650
v0 of
      C_IsRing'46'constructor_95033 T_IsAbelianGroup_1132
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_IsRing_2650
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.*-assoc
d_'42''45'assoc_2676 ::
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2676 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2676 T_IsRing_2650
v0
  = case T_IsRing_2650 -> T_IsRing_2650
forall a b. a -> b
coe T_IsRing_2650
v0 of
      C_IsRing'46'constructor_95033 T_IsAbelianGroup_1132
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_IsRing_2650
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.*-identity
d_'42''45'identity_2678 ::
  T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2678 :: T_IsRing_2650 -> T_Σ_14
d_'42''45'identity_2678 T_IsRing_2650
v0
  = case T_IsRing_2650 -> T_IsRing_2650
forall a b. a -> b
coe T_IsRing_2650
v0 of
      C_IsRing'46'constructor_95033 T_IsAbelianGroup_1132
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_IsRing_2650
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.distrib
d_distrib_2680 ::
  T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2680 :: T_IsRing_2650 -> T_Σ_14
d_distrib_2680 T_IsRing_2650
v0
  = case T_IsRing_2650 -> T_IsRing_2650
forall a b. a -> b
coe T_IsRing_2650
v0 of
      C_IsRing'46'constructor_95033 T_IsAbelianGroup_1132
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_IsRing_2650
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.isRingWithoutOne
d_isRingWithoutOne_2682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_2682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsRingWithoutOne_2286
d_isRingWithoutOne_2682 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 T_IsRing_2650
v9
du_isRingWithoutOne_2682 ::
  T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 :: T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 T_IsRing_2650
v0
  = (T_IsAbelianGroup_1132
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_IsRingWithoutOne_2286)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsRingWithoutOne_2286
forall a b. a -> b
coe
      T_IsAbelianGroup_1132
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_IsRingWithoutOne_2286
C_IsRingWithoutOne'46'constructor_75855
      ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
      ((T_IsRing_2650
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2674 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
      ((T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2676 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)) ((T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_Σ_14
d_distrib_2680 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._._//_
d__'47''47'__2686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__2686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__2686 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 ~T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2686 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'47''47'__2686 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2686 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2686 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsRing._.∙-congʳ
d_'8729''45'cong'691'_2688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2688 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2688 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2688 T_IsRing_2650
v9
du_'8729''45'cong'691'_2688 ::
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2688 :: T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2688 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsRing._.∙-congˡ
d_'8729''45'cong'737'_2690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2690 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2690 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2690 T_IsRing_2650
v9
du_'8729''45'cong'737'_2690 ::
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2690 :: T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2690 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsRing._.*-isMagma
d_'42''45'isMagma_2692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsMagma_176
d_'42''45'isMagma_2692 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsMagma_176
d_'42''45'isMagma_2692 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsMagma_176
du_'42''45'isMagma_2692 T_IsRing_2650
v9
du_'42''45'isMagma_2692 :: T_IsRing_2650 -> T_IsMagma_176
du_'42''45'isMagma_2692 :: T_IsRing_2650 -> T_IsMagma_176
du_'42''45'isMagma_2692 T_IsRing_2650
v0
  = (T_IsRingWithoutOne_2286 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> T_IsMagma_176
du_'42''45'isMagma_2388 ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.*-isSemigroup
d_'42''45'isSemigroup_2694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2694 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2694 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2694 T_IsRing_2650
v9
du_'42''45'isSemigroup_2694 :: T_IsRing_2650 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2694 :: T_IsRing_2650 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2694 T_IsRing_2650
v0
  = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.assoc
d_assoc_2696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2696 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2696 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2696 T_IsRing_2650
v9
du_assoc_2696 ::
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2696 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2696 T_IsRing_2650
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))))
-- Algebra.Structures.IsRing._.comm
d_comm_2698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_2698 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2698 T_IsRing_2650
v9
du_comm_2698 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2698 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2698 T_IsRing_2650
v0
  = (T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.∙-cong
d_'8729''45'cong_2700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2700 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2700 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2700 T_IsRing_2650
v9
du_'8729''45'cong_2700 ::
  T_IsRing_2650 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2700 :: T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2700 T_IsRing_2650
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))))))
-- Algebra.Structures.IsRing._.∙-congʳ
d_'8729''45'cong'691'_2702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2702 T_IsRing_2650
v9
du_'8729''45'cong'691'_2702 ::
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2702 :: T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2702 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsRing._.∙-congˡ
d_'8729''45'cong'737'_2704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2704 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2704 T_IsRing_2650
v9
du_'8729''45'cong'737'_2704 ::
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2704 :: T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2704 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsRing._.identity
d_identity_2706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2706 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_Σ_14
d_identity_2706 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_Σ_14
du_identity_2706 T_IsRing_2650
v9
du_identity_2706 ::
  T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_2706 :: T_IsRing_2650 -> T_Σ_14
du_identity_2706 T_IsRing_2650
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))))
-- Algebra.Structures.IsRing._.identityʳ
d_identity'691'_2708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_identity'691'_2708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_identity'691'_2708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'691'_2708 T_IsRing_2650
v9
du_identity'691'_2708 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'691'_2708 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'691'_2708 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Structures.IsRing._.identityˡ
d_identity'737'_2710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_identity'737'_2710 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_identity'737'_2710 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'737'_2710 T_IsRing_2650
v9
du_identity'737'_2710 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'737'_2710 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'737'_2710 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Structures.IsRing._.isCommutativeMagma
d_isCommutativeMagma_2712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2712 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2712 T_IsRing_2650
v9
du_isCommutativeMagma_2712 ::
  T_IsRing_2650 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2712 :: T_IsRing_2650 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2712 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Structures.IsRing._.isCommutativeMonoid
d_isCommutativeMonoid_2714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2714 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2714 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2714 T_IsRing_2650
v9
du_isCommutativeMonoid_2714 ::
  T_IsRing_2650 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2714 :: T_IsRing_2650 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2714 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204
         ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_2716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2716 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2716 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                              T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2716 T_IsRing_2650
v9
du_isCommutativeSemigroup_2716 ::
  T_IsRing_2650 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2716 :: T_IsRing_2650 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2716 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
            ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Structures.IsRing._.isGroup
d_isGroup_2718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsGroup_1036
d_isGroup_2718 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsGroup_1036
d_isGroup_2718 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsGroup_1036
du_isGroup_2718 T_IsRing_2650
v9
du_isGroup_2718 :: T_IsRing_2650 -> T_IsGroup_1036
du_isGroup_2718 :: T_IsRing_2650 -> T_IsGroup_1036
du_isGroup_2718 T_IsRing_2650
v0
  = (T_IsAbelianGroup_1132 -> T_IsGroup_1036)
-> AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.isInvertibleMagma
d_isInvertibleMagma_2720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_2720 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_2720 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2720 T_IsRing_2650
v9
du_isInvertibleMagma_2720 ::
  T_IsRing_2650 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2720 :: T_IsRing_2650 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2720 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Structures.IsRing._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_2722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsRing_2650 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2722 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                               T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2722 T_IsRing_2650
v9
du_isInvertibleUnitalMagma_2722 ::
  T_IsRing_2650 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2722 :: T_IsRing_2650 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2722 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Structures.IsRing._.isMagma
d_isMagma_2724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsMagma_176
d_isMagma_2724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsMagma_176
d_isMagma_2724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsMagma_176
du_isMagma_2724 T_IsRing_2650
v9
du_isMagma_2724 :: T_IsRing_2650 -> T_IsMagma_176
du_isMagma_2724 :: T_IsRing_2650 -> T_IsMagma_176
du_isMagma_2724 T_IsRing_2650
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))))
-- Algebra.Structures.IsRing._.isMonoid
d_isMonoid_2726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsMonoid_686
d_isMonoid_2726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsMonoid_686
d_isMonoid_2726 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsMonoid_686
du_isMonoid_2726 T_IsRing_2650
v9
du_isMonoid_2726 :: T_IsRing_2650 -> T_IsMonoid_686
du_isMonoid_2726 :: T_IsRing_2650 -> T_IsMonoid_686
du_isMonoid_2726 T_IsRing_2650
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))
-- Algebra.Structures.IsRing._.isSemigroup
d_isSemigroup_2728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsSemigroup_472
d_isSemigroup_2728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemigroup_472
d_isSemigroup_2728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsSemigroup_472
du_isSemigroup_2728 T_IsRing_2650
v9
du_isSemigroup_2728 :: T_IsRing_2650 -> T_IsSemigroup_472
du_isSemigroup_2728 :: T_IsRing_2650 -> T_IsSemigroup_472
du_isSemigroup_2728 T_IsRing_2650
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))))
-- Algebra.Structures.IsRing._.isUnitalMagma
d_isUnitalMagma_2730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsUnitalMagma_642
d_isUnitalMagma_2730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsUnitalMagma_642
d_isUnitalMagma_2730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsUnitalMagma_642
du_isUnitalMagma_2730 T_IsRing_2650
v9
du_isUnitalMagma_2730 :: T_IsRing_2650 -> T_IsUnitalMagma_642
du_isUnitalMagma_2730 :: T_IsRing_2650 -> T_IsUnitalMagma_642
du_isUnitalMagma_2730 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Structures.IsRing._.⁻¹-cong
d_'8315''185''45'cong_2732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8315''185''45'cong_2732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_2732 T_IsRing_2650
v9
du_'8315''185''45'cong_2732 ::
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_2732 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_2732 T_IsRing_2650
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))
-- Algebra.Structures.IsRing._.inverse
d_inverse_2734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_Σ_14
d_inverse_2734 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_Σ_14
du_inverse_2734 T_IsRing_2650
v9
du_inverse_2734 ::
  T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_2734 :: T_IsRing_2650 -> T_Σ_14
du_inverse_2734 T_IsRing_2650
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_Σ_14
d_inverse_1052
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))
-- Algebra.Structures.IsRing._.inverseʳ
d_inverse'691'_2736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_inverse'691'_2736 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_inverse'691'_2736 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny
du_inverse'691'_2736 T_IsRing_2650
v9
du_inverse'691'_2736 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_inverse'691'_2736 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_inverse'691'_2736 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Structures.IsRing._.inverseˡ
d_inverse'737'_2738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_inverse'737'_2738 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_inverse'737'_2738 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny
du_inverse'737'_2738 T_IsRing_2650
v9
du_inverse'737'_2738 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_inverse'737'_2738 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_inverse'737'_2738 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Structures.IsRing._.distribʳ
d_distrib'691'_2740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2740 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2740 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2740 T_IsRing_2650
v9
du_distrib'691'_2740 ::
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2740 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2740 T_IsRing_2650
v0
  = (T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2380 ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.distribˡ
d_distrib'737'_2742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2742 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2742 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2742 T_IsRing_2650
v9
du_distrib'737'_2742 ::
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2742 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2742 T_IsRing_2650
v0
  = (T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2378 ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.isEquivalence
d_isEquivalence_2744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2744 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsEquivalence_26
d_isEquivalence_2744 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsEquivalence_26
du_isEquivalence_2744 T_IsRing_2650
v9
du_isEquivalence_2744 ::
  T_IsRing_2650 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2744 :: T_IsRing_2650 -> T_IsEquivalence_26
du_isEquivalence_2744 T_IsRing_2650
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))))))
-- Algebra.Structures.IsRing._.isPartialEquivalence
d_isPartialEquivalence_2746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2746 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2746 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2746 T_IsRing_2650
v9
du_isPartialEquivalence_2746 ::
  T_IsRing_2650 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2746 :: T_IsRing_2650 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2746 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))))))))
-- Algebra.Structures.IsRing._.refl
d_refl_2748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_refl_2748 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_refl_2748 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny
du_refl_2748 T_IsRing_2650
v9
du_refl_2748 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_refl_2748 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_refl_2748 T_IsRing_2650
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))))))
-- Algebra.Structures.IsRing._.reflexive
d_reflexive_2750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2750 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2750 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2750 T_IsRing_2650
v9
du_reflexive_2750 ::
  T_IsRing_2650 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2750 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2750 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6)) AgdaAny
v7))))))
-- Algebra.Structures.IsRing._.setoid
d_setoid_2752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2752 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_Setoid_44
d_setoid_2752 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_Setoid_44
du_setoid_2752 T_IsRing_2650
v9
du_setoid_2752 ::
  T_IsRing_2650 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2752 :: T_IsRing_2650 -> T_Setoid_44
du_setoid_2752 T_IsRing_2650
v0
  = let v1 :: t
v1 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Structures.IsRing._.sym
d_sym_2754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2754 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9 = T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2754 T_IsRing_2650
v9
du_sym_2754 ::
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2754 :: T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2754 T_IsRing_2650
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))))))
-- Algebra.Structures.IsRing._.trans
d_trans_2756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2756 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2756 T_IsRing_2650
v9
du_trans_2756 ::
  T_IsRing_2650 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2756 :: T_IsRing_2650
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2756 T_IsRing_2650
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))))))
-- Algebra.Structures.IsRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_2758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_2758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2758 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_unique'691''45''8315''185'_2758 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2758 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2758 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsRing_2650
v3
  = let v4 :: t
v4 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v5 :: T_IsAbelianGroup_1132
v5 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v5))))
-- Algebra.Structures.IsRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_2760 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_2760 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2760 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_unique'737''45''8315''185'_2760 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2760 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2760 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsRing_2650
v3
  = let v4 :: t
v4 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v5 :: T_IsAbelianGroup_1132
v5 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v5))))
-- Algebra.Structures.IsRing._.zero
d_zero_2762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_Σ_14
d_zero_2762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_Σ_14
du_zero_2762 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_zero_2762 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRing_2650 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_2762 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_Σ_14
du_zero_2762 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRing_2650
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
du_zero_2386 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4))
-- Algebra.Structures.IsRing._.zeroʳ
d_zero'691'_2764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_zero'691'_2764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_zero'691'_2764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
du_zero'691'_2764 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_zero'691'_2764 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
du_zero'691'_2764 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
du_zero'691'_2764 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRing_2650
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'691'_2384 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4))
-- Algebra.Structures.IsRing._.zeroˡ
d_zero'737'_2766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_zero'737'_2766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_zero'737'_2766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
du_zero'737'_2766 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_zero'737'_2766 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
du_zero'737'_2766 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
du_zero'737'_2766 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRing_2650
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'737'_2382 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4))
-- Algebra.Structures.IsRing.*-isMonoid
d_'42''45'isMonoid_2768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsMonoid_686
d_'42''45'isMonoid_2768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsMonoid_686
d_'42''45'isMonoid_2768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 T_IsRing_2650
v9
du_'42''45'isMonoid_2768 :: T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 :: T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 T_IsRing_2650
v0
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
C_IsMonoid'46'constructor_15873
      ((T_IsRingWithoutOne_2286 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))
      ((T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_Σ_14
d_'42''45'identity_2678 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.identityʳ
d_identity'691'_2772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_identity'691'_2772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_identity'691'_2772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'691'_2772 T_IsRing_2650
v9
du_identity'691'_2772 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'691'_2772 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'691'_2772 T_IsRing_2650
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing._.identityˡ
d_identity'737'_2774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> AgdaAny -> AgdaAny
d_identity'737'_2774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> AgdaAny
-> AgdaAny
d_identity'737'_2774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'737'_2774 T_IsRing_2650
v9
du_identity'737'_2774 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'737'_2774 :: T_IsRing_2650 -> AgdaAny -> AgdaAny
du_identity'737'_2774 T_IsRing_2650
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2776 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2776 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5
                                         ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2776 T_IsRing_2650
v9
du_isSemiringWithoutAnnihilatingZero_2776 ::
  T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2776 :: T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2776 T_IsRing_2650
v0
  = (T_IsCommutativeMonoid_736
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1468
C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811
      ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204
         ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0)))
      ((T_IsRing_2650
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2674 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
      ((T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2676 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
      ((T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_Σ_14
d_'42''45'identity_2678 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
      ((T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_Σ_14
d_distrib_2680 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v0))
-- Algebra.Structures.IsRing.isSemiring
d_isSemiring_2778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsSemiring_1570
d_isSemiring_2778 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
d_isSemiring_2778 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_isSemiring_2778 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRing_2650 -> T_IsSemiring_1570
du_isSemiring_2778 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRing_2650
v4
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_Σ_14 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_Σ_14 -> T_IsSemiring_1570
C_IsSemiring'46'constructor_48071
      ((T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2776 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
du_zero_2386 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4)))
-- Algebra.Structures.IsRing._.isNearSemiring
d_isNearSemiring_2782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsNearSemiring_1218
d_isNearSemiring_2782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsNearSemiring_1218
d_isNearSemiring_2782 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsNearSemiring_1218
du_isNearSemiring_2782 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_isNearSemiring_2782 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRing_2650 -> T_IsNearSemiring_1218
du_isNearSemiring_2782 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsNearSemiring_1218
du_isNearSemiring_2782 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRing_2650
v4
  = let v5 :: t
v5
          = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))
-- Algebra.Structures.IsRing._.isSemiringWithoutOne
d_isSemiringWithoutOne_2784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_2650 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsRing_2650
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2784 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v9
du_isSemiringWithoutOne_2784 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRing_2650 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2784 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2784 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsRing_2650
v4
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4))
-- Algebra.Structures.IsCommutativeRing
d_IsCommutativeRing_2796 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeRing_2796 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsCommutativeRing_2796
  = C_IsCommutativeRing'46'constructor_100945 T_IsRing_2650
                                              (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeRing.isRing
d_isRing_2812 :: T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 :: T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 T_IsCommutativeRing_2796
v0
  = case T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0 of
      C_IsCommutativeRing'46'constructor_100945 T_IsRing_2650
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsRing_2650 -> T_IsRing_2650
forall a b. a -> b
coe T_IsRing_2650
v1
      T_IsCommutativeRing_2796
_ -> T_IsRing_2650
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeRing.*-comm
d_'42''45'comm_2814 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2814 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2814 T_IsCommutativeRing_2796
v0
  = case T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0 of
      C_IsCommutativeRing'46'constructor_100945 T_IsRing_2650
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeRing_2796
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeRing._._//_
d__'47''47'__2818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__2818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__2818 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 ~T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2818 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'47''47'__2818 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2818 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2818 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsCommutativeRing._.*-assoc
d_'42''45'assoc_2820 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2820 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2820 T_IsCommutativeRing_2796
v0
  = (T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2676 ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.*-cong
d_'42''45'cong_2822 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2822 :: T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2822 T_IsCommutativeRing_2796
v0
  = (T_IsRing_2650
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2674 ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_2824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2824 T_IsCommutativeRing_2796
v9
du_'8729''45'cong'691'_2824 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2824 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2824 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Structures.IsCommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_2826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2826 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2826 T_IsCommutativeRing_2796
v9
du_'8729''45'cong'737'_2826 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2826 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2826 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Structures.IsCommutativeRing._.*-identity
d_'42''45'identity_2828 ::
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2828 :: T_IsCommutativeRing_2796 -> T_Σ_14
d_'42''45'identity_2828 T_IsCommutativeRing_2796
v0
  = (T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsRing_2650 -> T_Σ_14
d_'42''45'identity_2678 ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.identityʳ
d_identity'691'_2830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_identity'691'_2830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_identity'691'_2830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'691'_2830 T_IsCommutativeRing_2796
v9
du_identity'691'_2830 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'691'_2830 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'691'_2830 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.identityˡ
d_identity'737'_2832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_identity'737'_2832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_identity'737'_2832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'737'_2832 T_IsCommutativeRing_2796
v9
du_identity'737'_2832 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'737'_2832 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'737'_2832 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.*-isMagma
d_'42''45'isMagma_2834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsMagma_176
d_'42''45'isMagma_2834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsMagma_176
d_'42''45'isMagma_2834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsMagma_176
du_'42''45'isMagma_2834 T_IsCommutativeRing_2796
v9
du_'42''45'isMagma_2834 ::
  T_IsCommutativeRing_2796 -> T_IsMagma_176
du_'42''45'isMagma_2834 :: T_IsCommutativeRing_2796 -> T_IsMagma_176
du_'42''45'isMagma_2834 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsMagma_176
du_'42''45'isMagma_2388 ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.*-isMonoid
d_'42''45'isMonoid_2836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsMonoid_686
d_'42''45'isMonoid_2836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsMonoid_686
d_'42''45'isMonoid_2836 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsMonoid_686
du_'42''45'isMonoid_2836 T_IsCommutativeRing_2796
v9
du_'42''45'isMonoid_2836 ::
  T_IsCommutativeRing_2796 -> T_IsMonoid_686
du_'42''45'isMonoid_2836 :: T_IsCommutativeRing_2796 -> T_IsMonoid_686
du_'42''45'isMonoid_2836 T_IsCommutativeRing_2796
v0
  = (T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsRing_2650 -> T_IsMonoid_686
du_'42''45'isMonoid_2768 ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.*-isSemigroup
d_'42''45'isSemigroup_2838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2838 T_IsCommutativeRing_2796
v9
du_'42''45'isSemigroup_2838 ::
  T_IsCommutativeRing_2796 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2838 :: T_IsCommutativeRing_2796 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2838 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2390
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.assoc
d_assoc_2840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_2840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2840 T_IsCommutativeRing_2796
v9
du_assoc_2840 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2840 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_2840 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))
-- Algebra.Structures.IsCommutativeRing._.comm
d_comm_2842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_comm_2842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2842 T_IsCommutativeRing_2796
v9
du_comm_2842 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2842 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_2842 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.∙-cong
d_'8729''45'cong_2844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2844 T_IsCommutativeRing_2796
v9
du_'8729''45'cong_2844 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_2844 :: T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_2844 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))))
-- Algebra.Structures.IsCommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_2846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2846 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2846 T_IsCommutativeRing_2796
v9
du_'8729''45'cong'691'_2846 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2846 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2846 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsCommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_2848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2848 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2848 T_IsCommutativeRing_2796
v9
du_'8729''45'cong'737'_2848 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2848 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2848 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsCommutativeRing._.identity
d_identity_2850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_Σ_14
d_identity_2850 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_Σ_14
du_identity_2850 T_IsCommutativeRing_2796
v9
du_identity_2850 ::
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_2850 :: T_IsCommutativeRing_2796 -> T_Σ_14
du_identity_2850 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_Σ_14
d_identity_698
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))
-- Algebra.Structures.IsCommutativeRing._.identityʳ
d_identity'691'_2852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_identity'691'_2852 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_identity'691'_2852 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'691'_2852 T_IsCommutativeRing_2796
v9
du_identity'691'_2852 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'691'_2852 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'691'_2852 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v4))))))
-- Algebra.Structures.IsCommutativeRing._.identityˡ
d_identity'737'_2854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_identity'737'_2854 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_identity'737'_2854 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'737'_2854 T_IsCommutativeRing_2796
v9
du_identity'737'_2854 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'737'_2854 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_identity'737'_2854 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v4))))))
-- Algebra.Structures.IsCommutativeRing._.+-isAbelianGroup
d_'43''45'isAbelianGroup_2856 ::
  T_IsCommutativeRing_2796 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2856 :: T_IsCommutativeRing_2796 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2856 T_IsCommutativeRing_2796
v0
  = (T_IsRing_2650 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_2858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2858 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2858 T_IsCommutativeRing_2796
v9
du_isCommutativeMagma_2858 ::
  T_IsCommutativeRing_2796 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2858 :: T_IsCommutativeRing_2796 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2858 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
                  ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeMonoid
d_isCommutativeMonoid_2860 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2860 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_2860 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2860 T_IsCommutativeRing_2796
v9
du_isCommutativeMonoid_2860 ::
  T_IsCommutativeRing_2796 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2860 :: T_IsCommutativeRing_2796 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_2860 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204
            ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_2862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2862 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                              T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2862 T_IsCommutativeRing_2796
v9
du_isCommutativeSemigroup_2862 ::
  T_IsCommutativeRing_2796 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2862 :: T_IsCommutativeRing_2796 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2862 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
               ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Structures.IsCommutativeRing._.isGroup
d_isGroup_2864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsGroup_1036
d_isGroup_2864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsGroup_1036
d_isGroup_2864 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsGroup_1036
du_isGroup_2864 T_IsCommutativeRing_2796
v9
du_isGroup_2864 :: T_IsCommutativeRing_2796 -> T_IsGroup_1036
du_isGroup_2864 :: T_IsCommutativeRing_2796 -> T_IsGroup_1036
du_isGroup_2864 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.isInvertibleMagma
d_isInvertibleMagma_2866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_2866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_2866 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2866 T_IsCommutativeRing_2796
v9
du_isInvertibleMagma_2866 ::
  T_IsCommutativeRing_2796 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2866 :: T_IsCommutativeRing_2796 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_2866 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Structures.IsCommutativeRing._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_2868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2868 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_2868 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                               T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2868 T_IsCommutativeRing_2796
v9
du_isInvertibleUnitalMagma_2868 ::
  T_IsCommutativeRing_2796 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2868 :: T_IsCommutativeRing_2796 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_2868 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Structures.IsCommutativeRing._.isMagma
d_isMagma_2870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsMagma_176
d_isMagma_2870 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsMagma_176
d_isMagma_2870 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsMagma_176
du_isMagma_2870 T_IsCommutativeRing_2796
v9
du_isMagma_2870 :: T_IsCommutativeRing_2796 -> T_IsMagma_176
du_isMagma_2870 :: T_IsCommutativeRing_2796 -> T_IsMagma_176
du_isMagma_2870 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))
-- Algebra.Structures.IsCommutativeRing._.isMonoid
d_isMonoid_2872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsMonoid_686
d_isMonoid_2872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsMonoid_686
d_isMonoid_2872 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsMonoid_686
du_isMonoid_2872 T_IsCommutativeRing_2796
v9
du_isMonoid_2872 :: T_IsCommutativeRing_2796 -> T_IsMonoid_686
du_isMonoid_2872 :: T_IsCommutativeRing_2796 -> T_IsMonoid_686
du_isMonoid_2872 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))
-- Algebra.Structures.IsCommutativeRing._.isSemigroup
d_isSemigroup_2874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsSemigroup_472
d_isSemigroup_2874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemigroup_472
d_isSemigroup_2874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsSemigroup_472
du_isSemigroup_2874 T_IsCommutativeRing_2796
v9
du_isSemigroup_2874 ::
  T_IsCommutativeRing_2796 -> T_IsSemigroup_472
du_isSemigroup_2874 :: T_IsCommutativeRing_2796 -> T_IsSemigroup_472
du_isSemigroup_2874 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))
-- Algebra.Structures.IsCommutativeRing._.isUnitalMagma
d_isUnitalMagma_2876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsUnitalMagma_642
d_isUnitalMagma_2876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsUnitalMagma_642
d_isUnitalMagma_2876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsUnitalMagma_642
du_isUnitalMagma_2876 T_IsCommutativeRing_2796
v9
du_isUnitalMagma_2876 ::
  T_IsCommutativeRing_2796 -> T_IsUnitalMagma_642
du_isUnitalMagma_2876 :: T_IsCommutativeRing_2796 -> T_IsUnitalMagma_642
du_isUnitalMagma_2876 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v4))))))
-- Algebra.Structures.IsCommutativeRing._.⁻¹-cong
d_'8315''185''45'cong_2878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8315''185''45'cong_2878 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_2878 T_IsCommutativeRing_2796
v9
du_'8315''185''45'cong_2878 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_2878 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_2878 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))
-- Algebra.Structures.IsCommutativeRing._.inverse
d_inverse_2880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_Σ_14
d_inverse_2880 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_Σ_14
du_inverse_2880 T_IsCommutativeRing_2796
v9
du_inverse_2880 ::
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_2880 :: T_IsCommutativeRing_2796 -> T_Σ_14
du_inverse_2880 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_Σ_14
d_inverse_1052
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))
-- Algebra.Structures.IsCommutativeRing._.inverseʳ
d_inverse'691'_2882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_inverse'691'_2882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_inverse'691'_2882 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_inverse'691'_2882 T_IsCommutativeRing_2796
v9
du_inverse'691'_2882 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_inverse'691'_2882 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_inverse'691'_2882 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Structures.IsCommutativeRing._.inverseˡ
d_inverse'737'_2884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_inverse'737'_2884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_inverse'737'_2884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_inverse'737'_2884 T_IsCommutativeRing_2796
v9
du_inverse'737'_2884 ::
  T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_inverse'737'_2884 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_inverse'737'_2884 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Structures.IsCommutativeRing._.distrib
d_distrib_2886 ::
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2886 :: T_IsCommutativeRing_2796 -> T_Σ_14
d_distrib_2886 T_IsCommutativeRing_2796
v0 = (T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsRing_2650 -> T_Σ_14
d_distrib_2680 ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.distribʳ
d_distrib'691'_2888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2888 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2888 T_IsCommutativeRing_2796
v9
du_distrib'691'_2888 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2888 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2888 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2380 ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.distribˡ
d_distrib'737'_2890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2890 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2890 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2890 T_IsCommutativeRing_2796
v9
du_distrib'737'_2890 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2890 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2890 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2378 ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Structures.IsCommutativeRing._.isEquivalence
d_isEquivalence_2892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsEquivalence_26
d_isEquivalence_2892 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsEquivalence_26
du_isEquivalence_2892 T_IsCommutativeRing_2796
v9
du_isEquivalence_2892 ::
  T_IsCommutativeRing_2796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2892 :: T_IsCommutativeRing_2796 -> T_IsEquivalence_26
du_isEquivalence_2892 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))))
-- Algebra.Structures.IsCommutativeRing._.isNearSemiring
d_isNearSemiring_2894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsNearSemiring_1218
d_isNearSemiring_2894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsNearSemiring_1218
d_isNearSemiring_2894 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsNearSemiring_1218
du_isNearSemiring_2894 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_isNearSemiring_2894 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsNearSemiring_1218
du_isNearSemiring_2894 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsNearSemiring_1218
du_isNearSemiring_2894 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = let v5 :: T_IsRing_2650
v5 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v6 :: t
v6
             = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
                 (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))
-- Algebra.Structures.IsCommutativeRing._.isPartialEquivalence
d_isPartialEquivalence_2896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2896 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2896 T_IsCommutativeRing_2796
v9
du_isPartialEquivalence_2896 ::
  T_IsCommutativeRing_2796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2896 :: T_IsCommutativeRing_2796 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2896 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)))))))))
-- Algebra.Structures.IsCommutativeRing._.isRingWithoutOne
d_isRingWithoutOne_2898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_2898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsRingWithoutOne_2286
d_isRingWithoutOne_2898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2898 T_IsCommutativeRing_2796
v9
du_isRingWithoutOne_2898 ::
  T_IsCommutativeRing_2796 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2898 :: T_IsCommutativeRing_2796 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2898 T_IsCommutativeRing_2796
v0
  = (T_IsRing_2650 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.isSemiring
d_isSemiring_2900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_2796 -> T_IsSemiring_1570
d_isSemiring_2900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemiring_1570
d_isSemiring_2900 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemiring_1570
du_isSemiring_2900 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_isSemiring_2900 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsSemiring_1570
du_isSemiring_2900 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemiring_1570
du_isSemiring_2900 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4))
-- Algebra.Structures.IsCommutativeRing._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2902 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2902 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5
                                         ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2902 T_IsCommutativeRing_2796
v9
du_isSemiringWithoutAnnihilatingZero_2902 ::
  T_IsCommutativeRing_2796 ->
  T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2902 :: T_IsCommutativeRing_2796
-> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2902 T_IsCommutativeRing_2796
v0
  = (T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_2776
      ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0))
-- Algebra.Structures.IsCommutativeRing._.isSemiringWithoutOne
d_isSemiringWithoutOne_2904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2904 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2904 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_isSemiringWithoutOne_2904 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2904 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2904 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = let v5 :: T_IsRing_2650
v5 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_1660
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))
-- Algebra.Structures.IsCommutativeRing._.refl
d_refl_2906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_refl_2906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_refl_2906 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_refl_2906 T_IsCommutativeRing_2796
v9
du_refl_2906 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_refl_2906 :: T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_refl_2906 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))))
-- Algebra.Structures.IsCommutativeRing._.reflexive
d_reflexive_2908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2908 T_IsCommutativeRing_2796
v9
du_reflexive_2908 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2908 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2908 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)) AgdaAny
v8)))))))
-- Algebra.Structures.IsCommutativeRing._.setoid
d_setoid_2910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_Setoid_44
d_setoid_2910 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796 -> T_Setoid_44
du_setoid_2910 T_IsCommutativeRing_2796
v9
du_setoid_2910 ::
  T_IsCommutativeRing_2796 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2910 :: T_IsCommutativeRing_2796 -> T_Setoid_44
du_setoid_2910 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Structures.IsCommutativeRing._.sym
d_sym_2912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2912 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9 = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2912 T_IsCommutativeRing_2796
v9
du_sym_2912 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2912 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2912 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))))
-- Algebra.Structures.IsCommutativeRing._.trans
d_trans_2914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2914 T_IsCommutativeRing_2796
v9
du_trans_2914 ::
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2914 :: T_IsCommutativeRing_2796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2914 T_IsCommutativeRing_2796
v0
  = let v1 :: T_IsRing_2650
v1 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2672 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))))
-- Algebra.Structures.IsCommutativeRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_2916 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_2916 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2916 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_unique'691''45''8315''185'_2916 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2916 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_2916 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsCommutativeRing_2796
v3
  = let v4 :: T_IsRing_2650
v4 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v5 :: t
v5 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v6 :: T_IsAbelianGroup_1132
v6 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v6)))))
-- Algebra.Structures.IsCommutativeRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2918 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_2918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_2918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2918 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_unique'737''45''8315''185'_2918 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeRing_2796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2918 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_2918 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsCommutativeRing_2796
v3
  = let v4 :: T_IsRing_2650
v4 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v5 :: t
v5 = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v6 :: T_IsAbelianGroup_1132
v6 = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2304 (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v6)))))
-- Algebra.Structures.IsCommutativeRing._.zero
d_zero_2920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_Σ_14
d_zero_2920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_Σ_14
du_zero_2920 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_zero_2920 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_2920 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_Σ_14
du_zero_2920 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = let v5 :: T_IsRing_2650
v5 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
du_zero_2386 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))
-- Algebra.Structures.IsCommutativeRing._.zeroʳ
d_zero'691'_2922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_zero'691'_2922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_zero'691'_2922 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
du_zero'691'_2922 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_zero'691'_2922 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_zero'691'_2922 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
du_zero'691'_2922 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = let v5 :: T_IsRing_2650
v5 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'691'_2384 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))
-- Algebra.Structures.IsCommutativeRing._.zeroˡ
d_zero'737'_2924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
d_zero'737'_2924 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
d_zero'737'_2924 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
du_zero'737'_2924 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_zero'737'_2924 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny
du_zero'737'_2924 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> AgdaAny
-> AgdaAny
du_zero'737'_2924 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = let v5 :: T_IsRing_2650
v5 = T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
du_zero'737'_2382 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))
-- Algebra.Structures.IsCommutativeRing.isCommutativeSemiring
d_isCommutativeSemiring_2926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2926 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2926 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_2926 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_isCommutativeSemiring_2926 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_2926 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_2926 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = (T_IsSemiring_1570
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe
      T_IsSemiring_1570
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1678
C_IsCommutativeSemiring'46'constructor_51895
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
du_isSemiring_2778 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4)))
      ((T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2814 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_2930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2930 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2930 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_2930 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_isCommutativeMagma_2930 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2930 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_2930 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = let v5 :: t
v5
          = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_2926 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
              (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v6 :: t
v6 = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
            ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))
-- Algebra.Structures.IsCommutativeRing._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_2932 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_2932 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_2932 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                   T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2932 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_'42''45'isCommutativeMonoid_2932 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2932 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2932 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = (T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_1788
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_2926 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4))
-- Algebra.Structures.IsCommutativeRing._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_2934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2934 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2934 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7
                                      ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2934 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_'42''45'isCommutativeSemigroup_2934 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeRing_2796 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2934 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2934 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = let v5 :: t
v5
          = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_2926 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
              (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454
         ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_2936 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2936 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2936 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7
                                       ~AgdaAny
v8 T_IsCommutativeRing_2796
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2936 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v9
du_isCommutativeSemiringWithoutOne_2936 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeRing_2796 -> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2936 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2936 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 T_IsCommutativeRing_2796
v4
  = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_1780
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_2926 ((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 -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4))
-- Algebra.Structures.IsQuasigroup
d_IsQuasigroup_2944 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasigroup_2944 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsQuasigroup_2944
  = C_IsQuasigroup'46'constructor_106057 T_IsMagma_176
                                         (AgdaAny ->
                                          AgdaAny ->
                                          AgdaAny -> 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.IsQuasigroup.isMagma
d_isMagma_2962 :: T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 :: T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 T_IsQuasigroup_2944
v0
  = case T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v0 of
      C_IsQuasigroup'46'constructor_106057 T_IsMagma_176
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsQuasigroup_2944
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasigroup.\\-cong
d_'92''92''45'cong_2964 ::
  T_IsQuasigroup_2944 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_2964 :: T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964 T_IsQuasigroup_2944
v0
  = case T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v0 of
      C_IsQuasigroup'46'constructor_106057 T_IsMagma_176
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
-> AgdaAny -> AgdaAny -> 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_IsQuasigroup_2944
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasigroup.//-cong
d_'47''47''45'cong_2966 ::
  T_IsQuasigroup_2944 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_2966 :: T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966 T_IsQuasigroup_2944
v0
  = case T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v0 of
      C_IsQuasigroup'46'constructor_106057 T_IsMagma_176
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
-> AgdaAny -> AgdaAny -> 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
v3
      T_IsQuasigroup_2944
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasigroup.leftDivides
d_leftDivides_2968 ::
  T_IsQuasigroup_2944 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_2968 :: T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968 T_IsQuasigroup_2944
v0
  = case T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v0 of
      C_IsQuasigroup'46'constructor_106057 T_IsMagma_176
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
-> AgdaAny -> AgdaAny -> 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_IsQuasigroup_2944
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasigroup.rightDivides
d_rightDivides_2970 ::
  T_IsQuasigroup_2944 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_2970 :: T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970 T_IsQuasigroup_2944
v0
  = case T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v0 of
      C_IsQuasigroup'46'constructor_106057 T_IsMagma_176
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
-> AgdaAny -> AgdaAny -> 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_IsQuasigroup_2944
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsQuasigroup._.isEquivalence
d_isEquivalence_2974 ::
  T_IsQuasigroup_2944 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2974 :: T_IsQuasigroup_2944 -> T_IsEquivalence_26
d_isEquivalence_2974 T_IsQuasigroup_2944
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup._.isPartialEquivalence
d_isPartialEquivalence_2976 ::
  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) ->
  T_IsQuasigroup_2944 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2976 T_IsQuasigroup_2944
v7
du_isPartialEquivalence_2976 ::
  T_IsQuasigroup_2944 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2976 :: T_IsQuasigroup_2944 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2976 T_IsQuasigroup_2944
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsQuasigroup._.refl
d_refl_2978 :: T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny
d_refl_2978 :: T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny
d_refl_2978 T_IsQuasigroup_2944
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0)))
-- Algebra.Structures.IsQuasigroup._.reflexive
d_reflexive_2980 ::
  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) ->
  T_IsQuasigroup_2944 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2980 T_IsQuasigroup_2944
v7
du_reflexive_2980 ::
  T_IsQuasigroup_2944 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2980 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2980 T_IsQuasigroup_2944
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsQuasigroup._.setoid
d_setoid_2982 ::
  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) ->
  T_IsQuasigroup_2944 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> T_Setoid_44
d_setoid_2982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7 = T_IsQuasigroup_2944 -> T_Setoid_44
du_setoid_2982 T_IsQuasigroup_2944
v7
du_setoid_2982 ::
  T_IsQuasigroup_2944 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2982 :: T_IsQuasigroup_2944 -> T_Setoid_44
du_setoid_2982 T_IsQuasigroup_2944
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup._.sym
d_sym_2984 ::
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2984 :: T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2984 T_IsQuasigroup_2944
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0)))
-- Algebra.Structures.IsQuasigroup._.trans
d_trans_2986 ::
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2986 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2986 T_IsQuasigroup_2944
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0)))
-- Algebra.Structures.IsQuasigroup._.∙-cong
d_'8729''45'cong_2988 ::
  T_IsQuasigroup_2944 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2988 :: T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2988 T_IsQuasigroup_2944
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup._.∙-congʳ
d_'8729''45'cong'691'_2990 ::
  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) ->
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2990 T_IsQuasigroup_2944
v7
du_'8729''45'cong'691'_2990 ::
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2990 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2990 T_IsQuasigroup_2944
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup._.∙-congˡ
d_'8729''45'cong'737'_2992 ::
  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) ->
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2992 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2992 T_IsQuasigroup_2944
v7
du_'8729''45'cong'737'_2992 ::
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2992 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2992 T_IsQuasigroup_2944
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup.\\-congˡ
d_'92''92''45'cong'737'_2994 ::
  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) ->
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_2994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_2994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9
                             AgdaAny
v10 AgdaAny
v11
  = T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 AgdaAny
v11
du_'92''92''45'cong'737'_2994 ::
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 T_IsQuasigroup_2944
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964 T_IsQuasigroup_2944
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Structures.IsQuasigroup.\\-congʳ
d_'92''92''45'cong'691'_2998 ::
  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) ->
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_2998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_2998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9
                             AgdaAny
v10 AgdaAny
v11
  = T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 AgdaAny
v11
du_'92''92''45'cong'691'_2998 ::
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 T_IsQuasigroup_2944
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964 T_IsQuasigroup_2944
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))) AgdaAny
v1)
-- Algebra.Structures.IsQuasigroup.//-congˡ
d_'47''47''45'cong'737'_3002 ::
  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) ->
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_3002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_3002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9
                             AgdaAny
v10 AgdaAny
v11
  = T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 AgdaAny
v11
du_'47''47''45'cong'737'_3002 ::
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 T_IsQuasigroup_2944
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966 T_IsQuasigroup_2944
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Structures.IsQuasigroup.//-congʳ
d_'47''47''45'cong'691'_3006 ::
  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) ->
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_3006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_3006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9
                             AgdaAny
v10 AgdaAny
v11
  = T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 T_IsQuasigroup_2944
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 AgdaAny
v11
du_'47''47''45'cong'691'_3006 ::
  T_IsQuasigroup_2944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 :: T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 T_IsQuasigroup_2944
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966 T_IsQuasigroup_2944
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))) AgdaAny
v1)
-- Algebra.Structures.IsQuasigroup.leftDividesˡ
d_leftDivides'737'_3010 ::
  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) ->
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_3010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'737'_3010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 T_IsQuasigroup_2944
v7
du_leftDivides'737'_3010 ::
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 :: T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 T_IsQuasigroup_2944
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_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup.leftDividesʳ
d_leftDivides'691'_3012 ::
  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) ->
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_3012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'691'_3012 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 T_IsQuasigroup_2944
v7
du_leftDivides'691'_3012 ::
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 :: T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 T_IsQuasigroup_2944
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_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup.rightDividesˡ
d_rightDivides'737'_3014 ::
  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) ->
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_3014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'737'_3014 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 T_IsQuasigroup_2944
v7
du_rightDivides'737'_3014 ::
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 :: T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 T_IsQuasigroup_2944
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_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsQuasigroup.rightDividesʳ
d_rightDivides'691'_3016 ::
  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) ->
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_3016 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'691'_3016 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsQuasigroup_2944
v7
  = T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 T_IsQuasigroup_2944
v7
du_rightDivides'691'_3016 ::
  T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 :: T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 T_IsQuasigroup_2944
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_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v0))
-- Algebra.Structures.IsLoop
d_IsLoop_3026 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLoop_3026 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsLoop_3026
  = C_IsLoop'46'constructor_111285 T_IsQuasigroup_2944
                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsLoop.isQuasigroup
d_isQuasigroup_3040 :: T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 :: T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 T_IsLoop_3026
v0
  = case T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v0 of
      C_IsLoop'46'constructor_111285 T_IsQuasigroup_2944
v1 T_Σ_14
v2 -> T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v1
      T_IsLoop_3026
_ -> T_IsQuasigroup_2944
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLoop.identity
d_identity_3042 ::
  T_IsLoop_3026 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3042 :: T_IsLoop_3026 -> T_Σ_14
d_identity_3042 T_IsLoop_3026
v0
  = case T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v0 of
      C_IsLoop'46'constructor_111285 T_IsQuasigroup_2944
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsLoop_3026
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLoop._.//-cong
d_'47''47''45'cong_3046 ::
  T_IsLoop_3026 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_3046 :: T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_3046 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.//-congʳ
d_'47''47''45'cong'691'_3048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_3048 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_3048 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3048 T_IsLoop_3026
v8
du_'47''47''45'cong'691'_3048 ::
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3048 :: T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3048 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.//-congˡ
d_'47''47''45'cong'737'_3050 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_3050 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_3050 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3050 T_IsLoop_3026
v8
du_'47''47''45'cong'737'_3050 ::
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3050 :: T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3050 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.\\-cong
d_'92''92''45'cong_3052 ::
  T_IsLoop_3026 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_3052 :: T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_3052 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.\\-congʳ
d_'92''92''45'cong'691'_3054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_3054 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_3054 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3054 T_IsLoop_3026
v8
du_'92''92''45'cong'691'_3054 ::
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3054 :: T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3054 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.\\-congˡ
d_'92''92''45'cong'737'_3056 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_3056 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_3056 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3056 T_IsLoop_3026
v8
du_'92''92''45'cong'737'_3056 ::
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3056 :: T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3056 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.isEquivalence
d_isEquivalence_3058 ::
  T_IsLoop_3026 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3058 :: T_IsLoop_3026 -> T_IsEquivalence_26
d_isEquivalence_3058 T_IsLoop_3026
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0)))
-- Algebra.Structures.IsLoop._.isMagma
d_isMagma_3060 :: T_IsLoop_3026 -> T_IsMagma_176
d_isMagma_3060 :: T_IsLoop_3026 -> T_IsMagma_176
d_isMagma_3060 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.isPartialEquivalence
d_isPartialEquivalence_3062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3062 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3062 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3062 T_IsLoop_3026
v8
du_isPartialEquivalence_3062 ::
  T_IsLoop_3026 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3062 :: T_IsLoop_3026 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3062 T_IsLoop_3026
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsLoop._.leftDivides
d_leftDivides_3064 ::
  T_IsLoop_3026 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_3064 :: T_IsLoop_3026 -> T_Σ_14
d_leftDivides_3064 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.leftDividesʳ
d_leftDivides'691'_3066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_3066 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'691'_3066 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3066 T_IsLoop_3026
v8
du_leftDivides'691'_3066 ::
  T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3066 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3066 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.leftDividesˡ
d_leftDivides'737'_3068 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_3068 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'737'_3068 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3068 T_IsLoop_3026
v8
du_leftDivides'737'_3068 ::
  T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3068 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3068 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.refl
d_refl_3070 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny
d_refl_3070 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny
d_refl_3070 T_IsLoop_3026
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))))
-- Algebra.Structures.IsLoop._.reflexive
d_reflexive_3072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3072 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3072 T_IsLoop_3026
v8
du_reflexive_3072 ::
  T_IsLoop_3026 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3072 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3072 T_IsLoop_3026
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsLoop._.rightDivides
d_rightDivides_3074 ::
  T_IsLoop_3026 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_3074 :: T_IsLoop_3026 -> T_Σ_14
d_rightDivides_3074 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.rightDividesʳ
d_rightDivides'691'_3076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_3076 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'691'_3076 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3076 T_IsLoop_3026
v8
du_rightDivides'691'_3076 ::
  T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3076 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3076 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.rightDividesˡ
d_rightDivides'737'_3078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_3078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'737'_3078 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3078 T_IsLoop_3026
v8
du_rightDivides'737'_3078 ::
  T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3078 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3078 T_IsLoop_3026
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop._.setoid
d_setoid_3080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_Setoid_44
d_setoid_3080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> T_Setoid_44
du_setoid_3080 T_IsLoop_3026
v8
du_setoid_3080 ::
  T_IsLoop_3026 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3080 :: T_IsLoop_3026 -> T_Setoid_44
du_setoid_3080 T_IsLoop_3026
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v1)))
-- Algebra.Structures.IsLoop._.sym
d_sym_3082 ::
  T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3082 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3082 T_IsLoop_3026
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))))
-- Algebra.Structures.IsLoop._.trans
d_trans_3084 ::
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3084 :: T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3084 T_IsLoop_3026
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))))
-- Algebra.Structures.IsLoop._.∙-cong
d_'8729''45'cong_3086 ::
  T_IsLoop_3026 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3086 :: T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3086 T_IsLoop_3026
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0)))
-- Algebra.Structures.IsLoop._.∙-congʳ
d_'8729''45'cong'691'_3088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3088 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3088 T_IsLoop_3026
v8
du_'8729''45'cong'691'_3088 ::
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3088 :: T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3088 T_IsLoop_3026
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v1)))
-- Algebra.Structures.IsLoop._.∙-congˡ
d_'8729''45'cong'737'_3090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3090 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3090 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3090 T_IsLoop_3026
v8
du_'8729''45'cong'737'_3090 ::
  T_IsLoop_3026 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3090 :: T_IsLoop_3026
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3090 T_IsLoop_3026
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v1)))
-- Algebra.Structures.IsLoop.identityˡ
d_identity'737'_3092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLoop_3026 -> AgdaAny -> AgdaAny
d_identity'737'_3092 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
d_identity'737'_3092 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'737'_3092 T_IsLoop_3026
v8
du_identity'737'_3092 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'737'_3092 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'737'_3092 T_IsLoop_3026
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_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_Σ_14
d_identity_3042 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLoop.identityʳ
d_identity'691'_3094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLoop_3026 -> AgdaAny -> AgdaAny
d_identity'691'_3094 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> AgdaAny
-> AgdaAny
d_identity'691'_3094 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLoop_3026
v8
  = T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'691'_3094 T_IsLoop_3026
v8
du_identity'691'_3094 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'691'_3094 :: T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'691'_3094 T_IsLoop_3026
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_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_Σ_14
d_identity_3042 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v0))
-- Algebra.Structures.IsLeftBolLoop
d_IsLeftBolLoop_3104 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLeftBolLoop_3104 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsLeftBolLoop_3104
  = C_IsLeftBolLoop'46'constructor_114283 T_IsLoop_3026
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsLeftBolLoop.isLoop
d_isLoop_3118 :: T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 :: T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 T_IsLeftBolLoop_3104
v0
  = case T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0 of
      C_IsLeftBolLoop'46'constructor_114283 T_IsLoop_3026
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1
      T_IsLeftBolLoop_3104
_ -> T_IsLoop_3026
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLeftBolLoop.leftBol
d_leftBol_3120 ::
  T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_3120 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_3120 T_IsLeftBolLoop_3104
v0
  = case T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0 of
      C_IsLeftBolLoop'46'constructor_114283 T_IsLoop_3026
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_IsLeftBolLoop_3104
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLeftBolLoop._.//-cong
d_'47''47''45'cong_3124 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_3124 :: T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_3124 T_IsLeftBolLoop_3104
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))
-- Algebra.Structures.IsLeftBolLoop._.//-congʳ
d_'47''47''45'cong'691'_3126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_3126 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_3126 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3126 T_IsLeftBolLoop_3104
v8
du_'47''47''45'cong'691'_3126 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3126 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3126 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.//-congˡ
d_'47''47''45'cong'737'_3128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_3128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_3128 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3128 T_IsLeftBolLoop_3104
v8
du_'47''47''45'cong'737'_3128 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3128 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3128 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.\\-cong
d_'92''92''45'cong_3130 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_3130 :: T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_3130 T_IsLeftBolLoop_3104
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))
-- Algebra.Structures.IsLeftBolLoop._.\\-congʳ
d_'92''92''45'cong'691'_3132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_3132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_3132 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3132 T_IsLeftBolLoop_3104
v8
du_'92''92''45'cong'691'_3132 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3132 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3132 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.\\-congˡ
d_'92''92''45'cong'737'_3134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_3134 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_3134 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3134 T_IsLeftBolLoop_3104
v8
du_'92''92''45'cong'737'_3134 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3134 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3134 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.identity
d_identity_3136 ::
  T_IsLeftBolLoop_3104 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3136 :: T_IsLeftBolLoop_3104 -> T_Σ_14
d_identity_3136 T_IsLeftBolLoop_3104
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLoop_3026 -> T_Σ_14
d_identity_3042 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0))
-- Algebra.Structures.IsLeftBolLoop._.identityʳ
d_identity'691'_3138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
d_identity'691'_3138 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
d_identity'691'_3138 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
du_identity'691'_3138 T_IsLeftBolLoop_3104
v8
du_identity'691'_3138 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
du_identity'691'_3138 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
du_identity'691'_3138 T_IsLeftBolLoop_3104
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'691'_3094 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0))
-- Algebra.Structures.IsLeftBolLoop._.identityˡ
d_identity'737'_3140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
d_identity'737'_3140 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
d_identity'737'_3140 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
du_identity'737'_3140 T_IsLeftBolLoop_3104
v8
du_identity'737'_3140 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
du_identity'737'_3140 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
du_identity'737'_3140 T_IsLeftBolLoop_3104
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'737'_3092 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0))
-- Algebra.Structures.IsLeftBolLoop._.isEquivalence
d_isEquivalence_3142 ::
  T_IsLeftBolLoop_3104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3142 :: T_IsLeftBolLoop_3104 -> T_IsEquivalence_26
d_isEquivalence_3142 T_IsLeftBolLoop_3104
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0))))
-- Algebra.Structures.IsLeftBolLoop._.isMagma
d_isMagma_3144 :: T_IsLeftBolLoop_3104 -> T_IsMagma_176
d_isMagma_3144 :: T_IsLeftBolLoop_3104 -> T_IsMagma_176
d_isMagma_3144 T_IsLeftBolLoop_3104
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))
-- Algebra.Structures.IsLeftBolLoop._.isPartialEquivalence
d_isPartialEquivalence_3146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3146 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3146 T_IsLeftBolLoop_3104
v8
du_isPartialEquivalence_3146 ::
  T_IsLeftBolLoop_3104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3146 :: T_IsLeftBolLoop_3104 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3146 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsLeftBolLoop._.isQuasigroup
d_isQuasigroup_3148 :: T_IsLeftBolLoop_3104 -> T_IsQuasigroup_2944
d_isQuasigroup_3148 :: T_IsLeftBolLoop_3104 -> T_IsQuasigroup_2944
d_isQuasigroup_3148 T_IsLeftBolLoop_3104
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0))
-- Algebra.Structures.IsLeftBolLoop._.leftDivides
d_leftDivides_3150 ::
  T_IsLeftBolLoop_3104 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_3150 :: T_IsLeftBolLoop_3104 -> T_Σ_14
d_leftDivides_3150 T_IsLeftBolLoop_3104
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))
-- Algebra.Structures.IsLeftBolLoop._.leftDividesʳ
d_leftDivides'691'_3152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_3152 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'691'_3152 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3152 T_IsLeftBolLoop_3104
v8
du_leftDivides'691'_3152 ::
  T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3152 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3152 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.leftDividesˡ
d_leftDivides'737'_3154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_3154 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'737'_3154 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3154 T_IsLeftBolLoop_3104
v8
du_leftDivides'737'_3154 ::
  T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3154 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3154 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.refl
d_refl_3156 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
d_refl_3156 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny
d_refl_3156 T_IsLeftBolLoop_3104
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))))
-- Algebra.Structures.IsLeftBolLoop._.reflexive
d_reflexive_3158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3158 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3158 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3158 T_IsLeftBolLoop_3104
v8
du_reflexive_3158 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3158 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3158 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsLeftBolLoop._.rightDivides
d_rightDivides_3160 ::
  T_IsLeftBolLoop_3104 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_3160 :: T_IsLeftBolLoop_3104 -> T_Σ_14
d_rightDivides_3160 T_IsLeftBolLoop_3104
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))
-- Algebra.Structures.IsLeftBolLoop._.rightDividesʳ
d_rightDivides'691'_3162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_3162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'691'_3162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3162 T_IsLeftBolLoop_3104
v8
du_rightDivides'691'_3162 ::
  T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3162 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3162 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.rightDividesˡ
d_rightDivides'737'_3164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_3164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'737'_3164 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3164 T_IsLeftBolLoop_3104
v8
du_rightDivides'737'_3164 ::
  T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3164 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3164 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsLeftBolLoop._.setoid
d_setoid_3166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> T_Setoid_44
d_setoid_3166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104 -> T_Setoid_44
du_setoid_3166 T_IsLeftBolLoop_3104
v8
du_setoid_3166 ::
  T_IsLeftBolLoop_3104 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3166 :: T_IsLeftBolLoop_3104 -> T_Setoid_44
du_setoid_3166 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsLeftBolLoop._.sym
d_sym_3168 ::
  T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3168 :: T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3168 T_IsLeftBolLoop_3104
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))))
-- Algebra.Structures.IsLeftBolLoop._.trans
d_trans_3170 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3170 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3170 T_IsLeftBolLoop_3104
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0)))))
-- Algebra.Structures.IsLeftBolLoop._.∙-cong
d_'8729''45'cong_3172 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3172 :: T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3172 T_IsLeftBolLoop_3104
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0))))
-- Algebra.Structures.IsLeftBolLoop._.∙-congʳ
d_'8729''45'cong'691'_3174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3174 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3174 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3174 T_IsLeftBolLoop_3104
v8
du_'8729''45'cong'691'_3174 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3174 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3174 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsLeftBolLoop._.∙-congˡ
d_'8729''45'cong'737'_3176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3176 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3176 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsLeftBolLoop_3104
v8
  = T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3176 T_IsLeftBolLoop_3104
v8
du_'8729''45'cong'737'_3176 ::
  T_IsLeftBolLoop_3104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3176 :: T_IsLeftBolLoop_3104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3176 T_IsLeftBolLoop_3104
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsRightBolLoop
d_IsRightBolLoop_3186 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRightBolLoop_3186 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsRightBolLoop_3186
  = C_IsRightBolLoop'46'constructor_116761 T_IsLoop_3026
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsRightBolLoop.isLoop
d_isLoop_3200 :: T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 :: T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 T_IsRightBolLoop_3186
v0
  = case T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0 of
      C_IsRightBolLoop'46'constructor_116761 T_IsLoop_3026
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1
      T_IsRightBolLoop_3186
_ -> T_IsLoop_3026
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRightBolLoop.rightBol
d_rightBol_3202 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_3202 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_3202 T_IsRightBolLoop_3186
v0
  = case T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0 of
      C_IsRightBolLoop'46'constructor_116761 T_IsLoop_3026
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_IsRightBolLoop_3186
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRightBolLoop._.//-cong
d_'47''47''45'cong_3206 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_3206 :: T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_3206 T_IsRightBolLoop_3186
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))
-- Algebra.Structures.IsRightBolLoop._.//-congʳ
d_'47''47''45'cong'691'_3208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_3208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_3208 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3208 T_IsRightBolLoop_3186
v8
du_'47''47''45'cong'691'_3208 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3208 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3208 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.//-congˡ
d_'47''47''45'cong'737'_3210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_3210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_3210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3210 T_IsRightBolLoop_3186
v8
du_'47''47''45'cong'737'_3210 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3210 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3210 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.\\-cong
d_'92''92''45'cong_3212 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_3212 :: T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_3212 T_IsRightBolLoop_3186
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))
-- Algebra.Structures.IsRightBolLoop._.\\-congʳ
d_'92''92''45'cong'691'_3214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_3214 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_3214 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3214 T_IsRightBolLoop_3186
v8
du_'92''92''45'cong'691'_3214 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3214 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3214 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.\\-congˡ
d_'92''92''45'cong'737'_3216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_3216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_3216 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3216 T_IsRightBolLoop_3186
v8
du_'92''92''45'cong'737'_3216 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3216 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3216 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.identity
d_identity_3218 ::
  T_IsRightBolLoop_3186 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3218 :: T_IsRightBolLoop_3186 -> T_Σ_14
d_identity_3218 T_IsRightBolLoop_3186
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLoop_3026 -> T_Σ_14
d_identity_3042 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0))
-- Algebra.Structures.IsRightBolLoop._.identityʳ
d_identity'691'_3220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
d_identity'691'_3220 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
d_identity'691'_3220 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
du_identity'691'_3220 T_IsRightBolLoop_3186
v8
du_identity'691'_3220 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
du_identity'691'_3220 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
du_identity'691'_3220 T_IsRightBolLoop_3186
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'691'_3094 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0))
-- Algebra.Structures.IsRightBolLoop._.identityˡ
d_identity'737'_3222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
d_identity'737'_3222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
d_identity'737'_3222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
du_identity'737'_3222 T_IsRightBolLoop_3186
v8
du_identity'737'_3222 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
du_identity'737'_3222 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
du_identity'737'_3222 T_IsRightBolLoop_3186
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'737'_3092 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0))
-- Algebra.Structures.IsRightBolLoop._.isEquivalence
d_isEquivalence_3224 ::
  T_IsRightBolLoop_3186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3224 :: T_IsRightBolLoop_3186 -> T_IsEquivalence_26
d_isEquivalence_3224 T_IsRightBolLoop_3186
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0))))
-- Algebra.Structures.IsRightBolLoop._.isMagma
d_isMagma_3226 :: T_IsRightBolLoop_3186 -> T_IsMagma_176
d_isMagma_3226 :: T_IsRightBolLoop_3186 -> T_IsMagma_176
d_isMagma_3226 T_IsRightBolLoop_3186
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))
-- Algebra.Structures.IsRightBolLoop._.isPartialEquivalence
d_isPartialEquivalence_3228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3228 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3228 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3228 T_IsRightBolLoop_3186
v8
du_isPartialEquivalence_3228 ::
  T_IsRightBolLoop_3186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3228 :: T_IsRightBolLoop_3186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3228 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsRightBolLoop._.isQuasigroup
d_isQuasigroup_3230 :: T_IsRightBolLoop_3186 -> T_IsQuasigroup_2944
d_isQuasigroup_3230 :: T_IsRightBolLoop_3186 -> T_IsQuasigroup_2944
d_isQuasigroup_3230 T_IsRightBolLoop_3186
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0))
-- Algebra.Structures.IsRightBolLoop._.leftDivides
d_leftDivides_3232 ::
  T_IsRightBolLoop_3186 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_3232 :: T_IsRightBolLoop_3186 -> T_Σ_14
d_leftDivides_3232 T_IsRightBolLoop_3186
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))
-- Algebra.Structures.IsRightBolLoop._.leftDividesʳ
d_leftDivides'691'_3234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_3234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'691'_3234 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3234 T_IsRightBolLoop_3186
v8
du_leftDivides'691'_3234 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3234 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3234 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.leftDividesˡ
d_leftDivides'737'_3236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_3236 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'737'_3236 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3236 T_IsRightBolLoop_3186
v8
du_leftDivides'737'_3236 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3236 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3236 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.refl
d_refl_3238 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
d_refl_3238 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny
d_refl_3238 T_IsRightBolLoop_3186
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))))
-- Algebra.Structures.IsRightBolLoop._.reflexive
d_reflexive_3240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3240 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3240 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3240 T_IsRightBolLoop_3186
v8
du_reflexive_3240 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3240 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3240 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsRightBolLoop._.rightDivides
d_rightDivides_3242 ::
  T_IsRightBolLoop_3186 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_3242 :: T_IsRightBolLoop_3186 -> T_Σ_14
d_rightDivides_3242 T_IsRightBolLoop_3186
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))
-- Algebra.Structures.IsRightBolLoop._.rightDividesʳ
d_rightDivides'691'_3244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_3244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'691'_3244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3244 T_IsRightBolLoop_3186
v8
du_rightDivides'691'_3244 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3244 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3244 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.rightDividesˡ
d_rightDivides'737'_3246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_3246 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'737'_3246 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3246 T_IsRightBolLoop_3186
v8
du_rightDivides'737'_3246 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3246 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3246 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsRightBolLoop._.setoid
d_setoid_3248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3248 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> T_Setoid_44
d_setoid_3248 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186 -> T_Setoid_44
du_setoid_3248 T_IsRightBolLoop_3186
v8
du_setoid_3248 ::
  T_IsRightBolLoop_3186 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3248 :: T_IsRightBolLoop_3186 -> T_Setoid_44
du_setoid_3248 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsRightBolLoop._.sym
d_sym_3250 ::
  T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3250 :: T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3250 T_IsRightBolLoop_3186
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))))
-- Algebra.Structures.IsRightBolLoop._.trans
d_trans_3252 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3252 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3252 T_IsRightBolLoop_3186
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0)))))
-- Algebra.Structures.IsRightBolLoop._.∙-cong
d_'8729''45'cong_3254 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3254 :: T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3254 T_IsRightBolLoop_3186
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0))))
-- Algebra.Structures.IsRightBolLoop._.∙-congʳ
d_'8729''45'cong'691'_3256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3256 T_IsRightBolLoop_3186
v8
du_'8729''45'cong'691'_3256 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3256 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3256 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsRightBolLoop._.∙-congˡ
d_'8729''45'cong'737'_3258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3258 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRightBolLoop_3186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3258 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsRightBolLoop_3186
v8
  = T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3258 T_IsRightBolLoop_3186
v8
du_'8729''45'cong'737'_3258 ::
  T_IsRightBolLoop_3186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3258 :: T_IsRightBolLoop_3186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3258 T_IsRightBolLoop_3186
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsMoufangLoop
d_IsMoufangLoop_3268 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMoufangLoop_3268 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsMoufangLoop_3268
  = C_IsMoufangLoop'46'constructor_119263 T_IsLeftBolLoop_3104
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMoufangLoop.isLeftBolLoop
d_isLeftBolLoop_3284 ::
  T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 :: T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 T_IsMoufangLoop_3268
v0
  = case T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0 of
      C_IsMoufangLoop'46'constructor_119263 T_IsLeftBolLoop_3104
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1
      T_IsMoufangLoop_3268
_ -> T_IsLeftBolLoop_3104
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMoufangLoop.rightBol
d_rightBol_3286 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_3286 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_3286 T_IsMoufangLoop_3268
v0
  = case T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0 of
      C_IsMoufangLoop'46'constructor_119263 T_IsLeftBolLoop_3104
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMoufangLoop_3268
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMoufangLoop.identical
d_identical_3288 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_identical_3288 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_identical_3288 T_IsMoufangLoop_3268
v0
  = case T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0 of
      C_IsMoufangLoop'46'constructor_119263 T_IsLeftBolLoop_3104
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
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_IsMoufangLoop_3268
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMoufangLoop._.//-cong
d_'47''47''45'cong_3292 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_3292 :: T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_3292 T_IsMoufangLoop_3268
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))
-- Algebra.Structures.IsMoufangLoop._.//-congʳ
d_'47''47''45'cong'691'_3294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_3294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_3294 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3294 T_IsMoufangLoop_3268
v8
du_'47''47''45'cong'691'_3294 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3294 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3294 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.//-congˡ
d_'47''47''45'cong'737'_3296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_3296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_3296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3296 T_IsMoufangLoop_3268
v8
du_'47''47''45'cong'737'_3296 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3296 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3296 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.\\-cong
d_'92''92''45'cong_3298 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_3298 :: T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_3298 T_IsMoufangLoop_3268
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))
-- Algebra.Structures.IsMoufangLoop._.\\-congʳ
d_'92''92''45'cong'691'_3300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_3300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_3300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3300 T_IsMoufangLoop_3268
v8
du_'92''92''45'cong'691'_3300 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3300 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3300 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.\\-congˡ
d_'92''92''45'cong'737'_3302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_3302 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_3302 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3302 T_IsMoufangLoop_3268
v8
du_'92''92''45'cong'737'_3302 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3302 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3302 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.identity
d_identity_3304 ::
  T_IsMoufangLoop_3268 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3304 :: T_IsMoufangLoop_3268 -> T_Σ_14
d_identity_3304 T_IsMoufangLoop_3268
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_Σ_14
d_identity_3042
      ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0)))
-- Algebra.Structures.IsMoufangLoop._.identityʳ
d_identity'691'_3306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
d_identity'691'_3306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
d_identity'691'_3306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
du_identity'691'_3306 T_IsMoufangLoop_3268
v8
du_identity'691'_3306 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
du_identity'691'_3306 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
du_identity'691'_3306 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'691'_3094 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1)))
-- Algebra.Structures.IsMoufangLoop._.identityˡ
d_identity'737'_3308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
d_identity'737'_3308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
d_identity'737'_3308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
du_identity'737'_3308 T_IsMoufangLoop_3268
v8
du_identity'737'_3308 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
du_identity'737'_3308 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
du_identity'737'_3308 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'737'_3092 ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1)))
-- Algebra.Structures.IsMoufangLoop._.isEquivalence
d_isEquivalence_3310 ::
  T_IsMoufangLoop_3268 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3310 :: T_IsMoufangLoop_3268 -> T_IsEquivalence_26
d_isEquivalence_3310 T_IsMoufangLoop_3268
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0)))))
-- Algebra.Structures.IsMoufangLoop._.isLoop
d_isLoop_3312 :: T_IsMoufangLoop_3268 -> T_IsLoop_3026
d_isLoop_3312 :: T_IsMoufangLoop_3268 -> T_IsLoop_3026
d_isLoop_3312 T_IsMoufangLoop_3268
v0
  = (T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))
-- Algebra.Structures.IsMoufangLoop._.isMagma
d_isMagma_3314 :: T_IsMoufangLoop_3268 -> T_IsMagma_176
d_isMagma_3314 :: T_IsMoufangLoop_3268 -> T_IsMagma_176
d_isMagma_3314 T_IsMoufangLoop_3268
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))
-- Algebra.Structures.IsMoufangLoop._.isPartialEquivalence
d_isPartialEquivalence_3316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3316 T_IsMoufangLoop_3268
v8
du_isPartialEquivalence_3316 ::
  T_IsMoufangLoop_3268 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3316 :: T_IsMoufangLoop_3268 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3316 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsMoufangLoop._.isQuasigroup
d_isQuasigroup_3318 :: T_IsMoufangLoop_3268 -> T_IsQuasigroup_2944
d_isQuasigroup_3318 :: T_IsMoufangLoop_3268 -> T_IsQuasigroup_2944
d_isQuasigroup_3318 T_IsMoufangLoop_3268
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
      ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0)))
-- Algebra.Structures.IsMoufangLoop._.leftBol
d_leftBol_3320 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_3320 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_3320 T_IsMoufangLoop_3268
v0
  = (T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_3120 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))
-- Algebra.Structures.IsMoufangLoop._.leftDivides
d_leftDivides_3322 ::
  T_IsMoufangLoop_3268 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_3322 :: T_IsMoufangLoop_3268 -> T_Σ_14
d_leftDivides_3322 T_IsMoufangLoop_3268
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))
-- Algebra.Structures.IsMoufangLoop._.leftDividesʳ
d_leftDivides'691'_3324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_3324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'691'_3324 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3324 T_IsMoufangLoop_3268
v8
du_leftDivides'691'_3324 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3324 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3324 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.leftDividesˡ
d_leftDivides'737'_3326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_3326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'737'_3326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3326 T_IsMoufangLoop_3268
v8
du_leftDivides'737'_3326 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3326 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3326 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.refl
d_refl_3328 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
d_refl_3328 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny
d_refl_3328 T_IsMoufangLoop_3268
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))))
-- Algebra.Structures.IsMoufangLoop._.reflexive
d_reflexive_3330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3330 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3330 T_IsMoufangLoop_3268
v8
du_reflexive_3330 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3330 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3330 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsMoufangLoop._.rightDivides
d_rightDivides_3332 ::
  T_IsMoufangLoop_3268 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_3332 :: T_IsMoufangLoop_3268 -> T_Σ_14
d_rightDivides_3332 T_IsMoufangLoop_3268
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))
-- Algebra.Structures.IsMoufangLoop._.rightDividesʳ
d_rightDivides'691'_3334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_3334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'691'_3334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3334 T_IsMoufangLoop_3268
v8
du_rightDivides'691'_3334 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3334 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3334 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.rightDividesˡ
d_rightDivides'737'_3336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_3336 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'737'_3336 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3336 T_IsMoufangLoop_3268
v8
du_rightDivides'737'_3336 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3336 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3336 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Structures.IsMoufangLoop._.setoid
d_setoid_3338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3338 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> T_Setoid_44
d_setoid_3338 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268 -> T_Setoid_44
du_setoid_3338 T_IsMoufangLoop_3268
v8
du_setoid_3338 ::
  T_IsMoufangLoop_3268 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3338 :: T_IsMoufangLoop_3268 -> T_Setoid_44
du_setoid_3338 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Structures.IsMoufangLoop._.sym
d_sym_3340 ::
  T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3340 :: T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3340 T_IsMoufangLoop_3268
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))))
-- Algebra.Structures.IsMoufangLoop._.trans
d_trans_3342 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3342 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3342 T_IsMoufangLoop_3268
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0))))))
-- Algebra.Structures.IsMoufangLoop._.∙-cong
d_'8729''45'cong_3344 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3344 :: T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3344 T_IsMoufangLoop_3268
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> AgdaAny
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0)))))
-- Algebra.Structures.IsMoufangLoop._.∙-congʳ
d_'8729''45'cong'691'_3346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3346 T_IsMoufangLoop_3268
v8
du_'8729''45'cong'691'_3346 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3346 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3346 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Structures.IsMoufangLoop._.∙-congˡ
d_'8729''45'cong'737'_3348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3348 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMoufangLoop_3268
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3348 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMoufangLoop_3268
v8
  = T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3348 T_IsMoufangLoop_3268
v8
du_'8729''45'cong'737'_3348 ::
  T_IsMoufangLoop_3268 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3348 :: T_IsMoufangLoop_3268
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3348 T_IsMoufangLoop_3268
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Structures.IsMiddleBolLoop
d_IsMiddleBolLoop_3358 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMiddleBolLoop_3358 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsMiddleBolLoop_3358
  = C_IsMiddleBolLoop'46'constructor_121973 T_IsLoop_3026
                                            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMiddleBolLoop.isLoop
d_isLoop_3372 :: T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 :: T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 T_IsMiddleBolLoop_3358
v0
  = case T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0 of
      C_IsMiddleBolLoop'46'constructor_121973 T_IsLoop_3026
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1
      T_IsMiddleBolLoop_3358
_ -> T_IsLoop_3026
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMiddleBolLoop.middleBol
d_middleBol_3374 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_middleBol_3374 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_middleBol_3374 T_IsMiddleBolLoop_3358
v0
  = case T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0 of
      C_IsMiddleBolLoop'46'constructor_121973 T_IsLoop_3026
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_IsMiddleBolLoop_3358
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMiddleBolLoop._.//-cong
d_'47''47''45'cong_3378 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_3378 :: T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_3378 T_IsMiddleBolLoop_3358
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))
-- Algebra.Structures.IsMiddleBolLoop._.//-congʳ
d_'47''47''45'cong'691'_3380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_3380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_3380 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3380 T_IsMiddleBolLoop_3358
v8
du_'47''47''45'cong'691'_3380 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3380 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3380 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_3006 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.//-congˡ
d_'47''47''45'cong'737'_3382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_3382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_3382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3382 T_IsMiddleBolLoop_3358
v8
du_'47''47''45'cong'737'_3382 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3382 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3382 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_3002 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.\\-cong
d_'92''92''45'cong_3384 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_3384 :: T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_3384 T_IsMiddleBolLoop_3358
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))
-- Algebra.Structures.IsMiddleBolLoop._.\\-congʳ
d_'92''92''45'cong'691'_3386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_3386 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_3386 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3386 T_IsMiddleBolLoop_3358
v8
du_'92''92''45'cong'691'_3386 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3386 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_3386 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_2998 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.\\-congˡ
d_'92''92''45'cong'737'_3388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_3388 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_3388 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3388 T_IsMiddleBolLoop_3358
v8
du_'92''92''45'cong'737'_3388 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3388 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_3388 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_2994 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.identity
d_identity_3390 ::
  T_IsMiddleBolLoop_3358 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3390 :: T_IsMiddleBolLoop_3358 -> T_Σ_14
d_identity_3390 T_IsMiddleBolLoop_3358
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLoop_3026 -> T_Σ_14
d_identity_3042 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0))
-- Algebra.Structures.IsMiddleBolLoop._.identityʳ
d_identity'691'_3392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
d_identity'691'_3392 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
d_identity'691'_3392 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
du_identity'691'_3392 T_IsMiddleBolLoop_3358
v8
du_identity'691'_3392 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
du_identity'691'_3392 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
du_identity'691'_3392 T_IsMiddleBolLoop_3358
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'691'_3094 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0))
-- Algebra.Structures.IsMiddleBolLoop._.identityˡ
d_identity'737'_3394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
d_identity'737'_3394 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
d_identity'737'_3394 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
du_identity'737'_3394 T_IsMiddleBolLoop_3358
v8
du_identity'737'_3394 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
du_identity'737'_3394 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
du_identity'737'_3394 T_IsMiddleBolLoop_3358
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> AgdaAny -> AgdaAny
du_identity'737'_3092 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0))
-- Algebra.Structures.IsMiddleBolLoop._.isEquivalence
d_isEquivalence_3396 ::
  T_IsMiddleBolLoop_3358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3396 :: T_IsMiddleBolLoop_3358 -> T_IsEquivalence_26
d_isEquivalence_3396 T_IsMiddleBolLoop_3358
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0))))
-- Algebra.Structures.IsMiddleBolLoop._.isMagma
d_isMagma_3398 :: T_IsMiddleBolLoop_3358 -> T_IsMagma_176
d_isMagma_3398 :: T_IsMiddleBolLoop_3358 -> T_IsMagma_176
d_isMagma_3398 T_IsMiddleBolLoop_3358
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))
-- Algebra.Structures.IsMiddleBolLoop._.isPartialEquivalence
d_isPartialEquivalence_3400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3400 T_IsMiddleBolLoop_3358
v8
du_isPartialEquivalence_3400 ::
  T_IsMiddleBolLoop_3358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3400 :: T_IsMiddleBolLoop_3358 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3400 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsMiddleBolLoop._.isQuasigroup
d_isQuasigroup_3402 ::
  T_IsMiddleBolLoop_3358 -> T_IsQuasigroup_2944
d_isQuasigroup_3402 :: T_IsMiddleBolLoop_3358 -> T_IsQuasigroup_2944
d_isQuasigroup_3402 T_IsMiddleBolLoop_3358
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0))
-- Algebra.Structures.IsMiddleBolLoop._.leftDivides
d_leftDivides_3404 ::
  T_IsMiddleBolLoop_3358 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_3404 :: T_IsMiddleBolLoop_3358 -> T_Σ_14
d_leftDivides_3404 T_IsMiddleBolLoop_3358
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))
-- Algebra.Structures.IsMiddleBolLoop._.leftDividesʳ
d_leftDivides'691'_3406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_3406 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'691'_3406 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3406 T_IsMiddleBolLoop_3358
v8
du_leftDivides'691'_3406 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3406 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3406 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_3012 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.leftDividesˡ
d_leftDivides'737'_3408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_3408 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_leftDivides'737'_3408 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3408 T_IsMiddleBolLoop_3358
v8
du_leftDivides'737'_3408 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3408 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3408 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_3010 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.refl
d_refl_3410 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
d_refl_3410 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny
d_refl_3410 T_IsMiddleBolLoop_3358
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))))
-- Algebra.Structures.IsMiddleBolLoop._.reflexive
d_reflexive_3412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3412 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3412 T_IsMiddleBolLoop_3358
v8
du_reflexive_3412 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3412 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3412 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsMiddleBolLoop._.rightDivides
d_rightDivides_3414 ::
  T_IsMiddleBolLoop_3358 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_3414 :: T_IsMiddleBolLoop_3358 -> T_Σ_14
d_rightDivides_3414 T_IsMiddleBolLoop_3358
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))
-- Algebra.Structures.IsMiddleBolLoop._.rightDividesʳ
d_rightDivides'691'_3416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_3416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'691'_3416 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3416 T_IsMiddleBolLoop_3358
v8
du_rightDivides'691'_3416 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3416 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3416 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_3016 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.rightDividesˡ
d_rightDivides'737'_3418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_3418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_rightDivides'737'_3418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3418 T_IsMiddleBolLoop_3358
v8
du_rightDivides'737'_3418 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3418 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3418 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_3014 ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Structures.IsMiddleBolLoop._.setoid
d_setoid_3420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> T_Setoid_44
d_setoid_3420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358 -> T_Setoid_44
du_setoid_3420 T_IsMiddleBolLoop_3358
v8
du_setoid_3420 ::
  T_IsMiddleBolLoop_3358 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3420 :: T_IsMiddleBolLoop_3358 -> T_Setoid_44
du_setoid_3420 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsMiddleBolLoop._.sym
d_sym_3422 ::
  T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3422 :: T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3422 T_IsMiddleBolLoop_3358
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))))
-- Algebra.Structures.IsMiddleBolLoop._.trans
d_trans_3424 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3424 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3424 T_IsMiddleBolLoop_3358
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0)))))
-- Algebra.Structures.IsMiddleBolLoop._.∙-cong
d_'8729''45'cong_3426 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3426 :: T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3426 T_IsMiddleBolLoop_3358
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0))))
-- Algebra.Structures.IsMiddleBolLoop._.∙-congʳ
d_'8729''45'cong'691'_3428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3428 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3428 T_IsMiddleBolLoop_3358
v8
du_'8729''45'cong'691'_3428 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3428 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3428 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Structures.IsMiddleBolLoop._.∙-congˡ
d_'8729''45'cong'737'_3430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMiddleBolLoop_3358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsMiddleBolLoop_3358
v8
  = T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3430 T_IsMiddleBolLoop_3358
v8
du_'8729''45'cong'737'_3430 ::
  T_IsMiddleBolLoop_3358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3430 :: T_IsMiddleBolLoop_3358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3430 T_IsMiddleBolLoop_3358
v0
  = let v1 :: T_IsLoop_3026
v1 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2 = T_IsLoop_3026 -> T_IsQuasigroup_2944
d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))