{-# 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.Function.Consequences.Setoid where

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

-- Function.Consequences.Setoid.S._≈_
d__'8776'__20 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__20 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__20 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Consequences.Setoid.S.Carrier
d_Carrier_24 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 -> ()
d_Carrier_24 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
d_Carrier_24 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
forall a. a
erased
-- Function.Consequences.Setoid.contraInjective
d_contraInjective_70 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_contraInjective_70 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> T_Irrelevant_20
d_contraInjective_70 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> T_Irrelevant_20
forall a. a
erased
-- Function.Consequences.Setoid.inverseˡ⇒surjective
d_inverse'737''8658'surjective_72 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse'737''8658'surjective_72 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Σ_14
d_inverse'737''8658'surjective_72 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Σ_14
du_inverse'737''8658'surjective_72 AgdaAny -> AgdaAny
v7
du_inverse'737''8658'surjective_72 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse'737''8658'surjective_72 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Σ_14
du_inverse'737''8658'surjective_72 AgdaAny -> AgdaAny
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Σ_14)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Consequences.du_inverse'737''8658'surjective_38
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0)
-- Function.Consequences.Setoid.inverseʳ⇒injective
d_inverse'691''8658'injective_76 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691''8658'injective_76 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_inverse'691''8658'injective_76 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
  = T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_inverse'691''8658'injective_76 T_Setoid_44
v4 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
du_inverse'691''8658'injective_76 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691''8658'injective_76 :: T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_inverse'691''8658'injective_76 T_Setoid_44
v0 T_Setoid_44
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3
  = ((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
      (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.Function.Consequences.du_inverse'691''8658'injective_50
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3)
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)))
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
-- Function.Consequences.Setoid.inverseᵇ⇒bijective
d_inverse'7495''8658'bijective_80 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse'7495''8658'bijective_80 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
d_inverse'7495''8658'bijective_80 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
  = T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
du_inverse'7495''8658'bijective_80 T_Setoid_44
v4 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
du_inverse'7495''8658'bijective_80 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse'7495''8658'bijective_80 :: T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
du_inverse'7495''8658'bijective_80 T_Setoid_44
v0 T_Setoid_44
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Σ_14)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_Σ_14
-> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
MAlonzo.Code.Function.Consequences.du_inverse'7495''8658'bijective_72
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3)
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)))
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
-- Function.Consequences.Setoid.surjective⇒strictlySurjective
d_surjective'8658'strictlySurjective_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective'8658'strictlySurjective_82 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> AgdaAny
-> T_Σ_14
d_surjective'8658'strictlySurjective_82 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6
  = T_Setoid_44 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
du_surjective'8658'strictlySurjective_82 T_Setoid_44
v4
du_surjective'8658'strictlySurjective_82 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_surjective'8658'strictlySurjective_82 :: T_Setoid_44 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
du_surjective'8658'strictlySurjective_82 T_Setoid_44
v0
  = ((AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14)
-> AgdaAny -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Consequences.du_surjective'8658'strictlySurjective_90
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
-- Function.Consequences.Setoid.strictlySurjective⇒surjective
d_strictlySurjective'8658'surjective_84 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective'8658'surjective_84 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> AgdaAny
-> T_Σ_14
d_strictlySurjective'8658'surjective_84 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6
  = T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> AgdaAny
-> T_Σ_14
du_strictlySurjective'8658'surjective_84 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6
du_strictlySurjective'8658'surjective_84 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective'8658'surjective_84 :: T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> AgdaAny
-> T_Σ_14
du_strictlySurjective'8658'surjective_84 T_Setoid_44
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> AgdaAny
 -> T_Σ_14)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> AgdaAny
-> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> AgdaAny
-> T_Σ_14
MAlonzo.Code.Function.Consequences.du_strictlySurjective'8658'surjective_100
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
-- Function.Consequences.Setoid.inverseˡ⇒strictlyInverseˡ
d_inverse'737''8658'strictlyInverse'737'_86 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_inverse'737''8658'strictlyInverse'737'_86 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
d_inverse'737''8658'strictlyInverse'737'_86 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 ~T_Setoid_44
v5
                                            ~AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
  = T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_inverse'737''8658'strictlyInverse'737'_86 T_Setoid_44
v4 AgdaAny -> AgdaAny
v7
du_inverse'737''8658'strictlyInverse'737'_86 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
du_inverse'737''8658'strictlyInverse'737'_86 :: T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_inverse'737''8658'strictlyInverse'737'_86 T_Setoid_44
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Function.Consequences.du_inverse'737''8658'strictlyInverse'737'_118
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
-- Function.Consequences.Setoid.strictlyInverseˡ⇒inverseˡ
d_strictlyInverse'737''8658'inverse'737'_88 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_strictlyInverse'737''8658'inverse'737'_88 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737''8658'inverse'737'_88 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 T_Setoid_44
v5
                                            AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
  = T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_strictlyInverse'737''8658'inverse'737'_88 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
du_strictlyInverse'737''8658'inverse'737'_88 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_strictlyInverse'737''8658'inverse'737'_88 :: T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_strictlyInverse'737''8658'inverse'737'_88 T_Setoid_44
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2
  = ((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
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Function.Consequences.du_strictlyInverse'737''8658'inverse'737'_126
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
-- Function.Consequences.Setoid.inverseʳ⇒strictlyInverseʳ
d_inverse'691''8658'strictlyInverse'691'_90 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_inverse'691''8658'strictlyInverse'691'_90 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
d_inverse'691''8658'strictlyInverse'691'_90 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 T_Setoid_44
v5
                                            AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7
  = T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_inverse'691''8658'strictlyInverse'691'_90 T_Setoid_44
v5 AgdaAny -> AgdaAny
v6
du_inverse'691''8658'strictlyInverse'691'_90 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
du_inverse'691''8658'strictlyInverse'691'_90 :: T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_inverse'691''8658'strictlyInverse'691'_90 T_Setoid_44
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Function.Consequences.du_inverse'691''8658'strictlyInverse'691'_142
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))
-- Function.Consequences.Setoid.strictlyInverseʳ⇒inverseʳ
d_strictlyInverse'691''8658'inverse'691'_92 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_strictlyInverse'691''8658'inverse'691'_92 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691''8658'inverse'691'_92 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 ~T_Setoid_44
v5
                                            AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
  = T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_strictlyInverse'691''8658'inverse'691'_92 T_Setoid_44
v4 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7
du_strictlyInverse'691''8658'inverse'691'_92 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_strictlyInverse'691''8658'inverse'691'_92 :: T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_strictlyInverse'691''8658'inverse'691'_92 T_Setoid_44
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2
  = ((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
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Function.Consequences.du_strictlyInverse'691''8658'inverse'691'_150
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
      ((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 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)))