{-# 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.Bundles 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.Function.Consequences.Propositional
import qualified MAlonzo.Code.Function.Structures
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Function.Bundles._._._≈_
d__'8776'__30 ::
  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'__30 :: 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'__30 = 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.Bundles._._.Carrier
d_Carrier_32 ::
  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_32 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
d_Carrier_32 = 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.Bundles._._.IsBijection
d_IsBijection_46 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBijection_46 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsCongruent
d_IsCongruent_48 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCongruent_48 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsInjection
d_IsInjection_50 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInjection_50 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsSurjection
d_IsSurjection_60 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSurjection_60 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsBijection.isInjection
d_isInjection_204 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
d_isInjection_204 :: T_IsBijection_238 -> T_IsInjection_92
d_isInjection_204 T_IsBijection_238
v0
  = (T_IsBijection_238 -> T_IsInjection_92)
-> AgdaAny -> T_IsInjection_92
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0)
-- Function.Bundles._._.IsBijection.surjective
d_surjective_210 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_210 :: T_IsBijection_238 -> AgdaAny -> T_Σ_14
d_surjective_210 T_IsBijection_238
v0
  = (T_IsBijection_238 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsBijection_238 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.d_surjective_248 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0)
-- Function.Bundles._._.IsBijection.Eq₁._≈_
d__'8776'__214 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__214 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__214 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁._≉_
d__'8777'__216 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__216 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁.Carrier
d_Carrier_218 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 -> ()
d_Carrier_218 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Level_18
d_Carrier_218 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁.isEquivalence
d_isEquivalence_220 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_220 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsEquivalence_26
d_isEquivalence_220 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_220 T_IsBijection_238
v7
du_isEquivalence_220 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_220 :: T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_220 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsBijection.Eq₁.isPartialEquivalence
d_isPartialEquivalence_222 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_222 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_222 T_IsBijection_238
v7
du_isPartialEquivalence_222 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_222 :: T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_222 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3)))))
-- Function.Bundles._._.IsBijection.Eq₁.partialSetoid
d_partialSetoid_224 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_PartialSetoid_10
d_partialSetoid_224 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_224 T_IsBijection_238
v7
du_partialSetoid_224 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_224 :: T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_224 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₁.refl
d_refl_226 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny
d_refl_226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
d_refl_226 ~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_IsBijection_238
v7 = T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_226 T_IsBijection_238
v7
du_refl_226 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny
du_refl_226 :: T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_226 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₁.reflexive
d_reflexive_228 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_228 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_228 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_228 T_IsBijection_238
v7
du_reflexive_228 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_228 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_228 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsBijection.Eq₁.setoid
d_setoid_230 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_230 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Setoid_44
d_setoid_230 ~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_IsBijection_238
v7 = T_IsBijection_238 -> T_Setoid_44
du_setoid_230 T_IsBijection_238
v7
du_setoid_230 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_230 :: T_IsBijection_238 -> T_Setoid_44
du_setoid_230 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v1)))
-- Function.Bundles._._.IsBijection.Eq₁.sym
d_sym_232 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_232 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_232 ~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_IsBijection_238
v7 = T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_232 T_IsBijection_238
v7
du_sym_232 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_232 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_232 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsBijection.Eq₁.trans
d_trans_234 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_234 ~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_IsBijection_238
v7 = T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_234 T_IsBijection_238
v7
du_trans_234 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_234 :: T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_234 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsBijection.Eq₂._≈_
d__'8776'__238 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__238 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__238 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂._≉_
d__'8777'__240 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__240 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__240 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂.Carrier
d_Carrier_242 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 -> ()
d_Carrier_242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Level_18
d_Carrier_242 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂.isEquivalence
d_isEquivalence_244 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsEquivalence_26
d_isEquivalence_244 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_244 T_IsBijection_238
v7
du_isEquivalence_244 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_244 :: T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_244 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsBijection.Eq₂.isPartialEquivalence
d_isPartialEquivalence_246 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_246 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_246 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_246 T_IsBijection_238
v7
du_isPartialEquivalence_246 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_246 :: T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_246 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3)))))
-- Function.Bundles._._.IsBijection.Eq₂.partialSetoid
d_partialSetoid_248 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_248 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_PartialSetoid_10
d_partialSetoid_248 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_248 T_IsBijection_238
v7
du_partialSetoid_248 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_248 :: T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_248 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₂.refl
d_refl_250 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny
d_refl_250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
d_refl_250 ~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_IsBijection_238
v7 = T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_250 T_IsBijection_238
v7
du_refl_250 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny
du_refl_250 :: T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_250 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₂.reflexive
d_reflexive_252 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_252 ~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_IsBijection_238
v7
  = T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_252 T_IsBijection_238
v7
du_reflexive_252 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_252 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_252 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsBijection.Eq₂.setoid
d_setoid_254 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Setoid_44
d_setoid_254 ~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_IsBijection_238
v7 = T_IsBijection_238 -> T_Setoid_44
du_setoid_254 T_IsBijection_238
v7
du_setoid_254 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_254 :: T_IsBijection_238 -> T_Setoid_44
du_setoid_254 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v1)))
-- Function.Bundles._._.IsBijection.Eq₂.sym
d_sym_256 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_256 ~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_IsBijection_238
v7 = T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_256 T_IsBijection_238
v7
du_sym_256 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_256 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_256 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsBijection.Eq₂.trans
d_trans_258 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_258 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_258 ~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_IsBijection_238
v7 = T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_258 T_IsBijection_238
v7
du_trans_258 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_258 :: T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_258 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsCongruent.cong
d_cong_262 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_262 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_262 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_cong_32 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.isEquivalence₁
d_isEquivalence'8321'_264 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_264 :: T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_264 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.isEquivalence₂
d_isEquivalence'8322'_266 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_266 :: T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_266 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.Eq₁._≈_
d__'8776'__270 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__270 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₁._≉_
d__'8777'__272 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__272 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__272 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₁.Carrier
d_Carrier_274 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 -> ()
d_Carrier_274 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
d_Carrier_274 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₁.isEquivalence
d_isEquivalence_276 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_26
d_isEquivalence_276 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_276 T_IsCongruent_22
v7
du_isEquivalence_276 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_276 :: T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_276 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.Eq₁.isPartialEquivalence
d_isPartialEquivalence_278 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_278 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_278 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_278 T_IsCongruent_22
v7
du_isPartialEquivalence_278 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_278 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_278 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)))
-- Function.Bundles._._.IsCongruent.Eq₁.partialSetoid
d_partialSetoid_280 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_280 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_280 T_IsCongruent_22
v7
du_partialSetoid_280 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_280 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_280 T_IsCongruent_22
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
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₁.refl
d_refl_282 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
d_refl_282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_282 ~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_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_282 T_IsCongruent_22
v7
du_refl_282 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
du_refl_282 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_282 T_IsCongruent_22
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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₁.reflexive
d_reflexive_284 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_284 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_284 T_IsCongruent_22
v7
du_reflexive_284 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_284 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_284 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)
-- Function.Bundles._._.IsCongruent.Eq₁.setoid
d_setoid_286 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_44
d_setoid_286 ~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) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_286
du_setoid_286 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_286 :: (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_286 AgdaAny -> AgdaAny
v0 T_IsCongruent_22
v1
  = (T_IsCongruent_22 -> T_Setoid_44)
-> T_IsCongruent_22 -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 T_IsCongruent_22
v1
-- Function.Bundles._._.IsCongruent.Eq₁.sym
d_sym_288 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_288 ~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_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_288 T_IsCongruent_22
v7
du_sym_288 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_288 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_288 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)))
-- Function.Bundles._._.IsCongruent.Eq₁.trans
d_trans_290 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_290 ~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_IsCongruent_22
v7 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_290 T_IsCongruent_22
v7
du_trans_290 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_290 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_290 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)))
-- Function.Bundles._._.IsCongruent.Eq₂._≈_
d__'8776'__294 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__294 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂._≉_
d__'8777'__296 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__296 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂.Carrier
d_Carrier_298 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 -> ()
d_Carrier_298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
d_Carrier_298 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂.isEquivalence
d_isEquivalence_300 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_26
d_isEquivalence_300 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_300 T_IsCongruent_22
v7
du_isEquivalence_300 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_300 :: T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_300 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.Eq₂.isPartialEquivalence
d_isPartialEquivalence_302 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_302 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_302 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_302 T_IsCongruent_22
v7
du_isPartialEquivalence_302 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_302 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_302 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)))
-- Function.Bundles._._.IsCongruent.Eq₂.partialSetoid
d_partialSetoid_304 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_304 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_304 T_IsCongruent_22
v7
du_partialSetoid_304 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_304 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_304 T_IsCongruent_22
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
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₂.refl
d_refl_306 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
d_refl_306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_306 ~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_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_306 T_IsCongruent_22
v7
du_refl_306 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
du_refl_306 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_306 T_IsCongruent_22
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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₂.reflexive
d_reflexive_308 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_308 ~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_IsCongruent_22
v7
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_308 T_IsCongruent_22
v7
du_reflexive_308 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_308 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_308 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)
-- Function.Bundles._._.IsCongruent.Eq₂.setoid
d_setoid_310 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_44
d_setoid_310 ~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) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_310
du_setoid_310 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_310 :: (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_310 AgdaAny -> AgdaAny
v0 T_IsCongruent_22
v1
  = (T_IsCongruent_22 -> T_Setoid_44)
-> T_IsCongruent_22 -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 T_IsCongruent_22
v1
-- Function.Bundles._._.IsCongruent.Eq₂.sym
d_sym_312 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_312 ~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_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_312 T_IsCongruent_22
v7
du_sym_312 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_312 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_312 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)))
-- Function.Bundles._._.IsCongruent.Eq₂.trans
d_trans_314 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_314 ~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_IsCongruent_22
v7 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_314 T_IsCongruent_22
v7
du_trans_314 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_314 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_314 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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)))
-- Function.Bundles._._.IsInjection.injective
d_injective_320 ::
  MAlonzo.Code.Function.Structures.T_IsInjection_92 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_320 :: T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_320 T_IsInjection_92
v0
  = (T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_injective_102 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v0)
-- Function.Bundles._._.IsInjection.isCongruent
d_isCongruent_322 ::
  MAlonzo.Code.Function.Structures.T_IsInjection_92 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_322 :: T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_322 T_IsInjection_92
v0
  = (T_IsInjection_92 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v0)
-- Function.Bundles._._.IsSurjection.isCongruent
d_isCongruent_656 ::
  MAlonzo.Code.Function.Structures.T_IsSurjection_162 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_656 :: T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_656 T_IsSurjection_162
v0
  = (T_IsSurjection_162 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsSurjection_162 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_170 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0)
-- Function.Bundles._._.IsSurjection.strictlySurjective
d_strictlySurjective_662 ::
  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) ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_662 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_662 ~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) -> T_IsSurjection_162 -> AgdaAny -> T_Σ_14
du_strictlySurjective_662
du_strictlySurjective_662 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_662 :: (AgdaAny -> AgdaAny) -> T_IsSurjection_162 -> AgdaAny -> T_Σ_14
du_strictlySurjective_662 AgdaAny -> AgdaAny
v0 T_IsSurjection_162
v1 AgdaAny
v2
  = (T_IsSurjection_162 -> AgdaAny -> T_Σ_14)
-> T_IsSurjection_162 -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSurjection_162 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_230 T_IsSurjection_162
v1 AgdaAny
v2
-- Function.Bundles._._.IsSurjection.surjective
d_surjective_664 ::
  MAlonzo.Code.Function.Structures.T_IsSurjection_162 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_664 :: T_IsSurjection_162 -> AgdaAny -> T_Σ_14
d_surjective_664 T_IsSurjection_162
v0
  = (T_IsSurjection_162 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSurjection_162 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.d_surjective_172 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0)
-- Function.Bundles._.Func
d_Func_714 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Func_714 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Func_714
  = C_Func'46'constructor_6307 (AgdaAny -> AgdaAny)
                               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Func.to
d_to_720 :: T_Func_714 -> AgdaAny -> AgdaAny
d_to_720 :: T_Func_714 -> AgdaAny -> AgdaAny
d_to_720 T_Func_714
v0
  = case T_Func_714 -> T_Func_714
forall a b. a -> b
coe T_Func_714
v0 of
      C_Func'46'constructor_6307 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Func_714
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Func.cong
d_cong_722 ::
  T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_722 :: T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_722 T_Func_714
v0
  = case T_Func_714 -> T_Func_714
forall a b. a -> b
coe T_Func_714
v0 of
      C_Func'46'constructor_6307 AgdaAny -> AgdaAny
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_Func_714
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Func.isCongruent
d_isCongruent_724 ::
  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 ->
  T_Func_714 -> MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_IsCongruent_22
d_isCongruent_724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_isCongruent_724 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 -> MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_724 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_722 (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2))
      ((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_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))
-- Function.Bundles._.Func._.Eq₁._≈_
d__'8776'__730 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> ()
d__'8776'__730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__730 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁._≉_
d__'8777'__732 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> ()
d__'8777'__732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__732 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁.Carrier
d_Carrier_734 ::
  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 ->
  T_Func_714 -> ()
d_Carrier_734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_Level_18
d_Carrier_734 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁.isEquivalence
d_isEquivalence_736 ::
  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 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_736 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_IsEquivalence_26
d_isEquivalence_736 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsEquivalence_26
du_isEquivalence_736 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_isEquivalence_736 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_736 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsEquivalence_26
du_isEquivalence_736 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.Func._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_738 ::
  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 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_738 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_738 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Func_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_738 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_isPartialEquivalence_738 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_738 :: T_Setoid_44
-> T_Setoid_44 -> T_Func_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_738 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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
v4))))
-- Function.Bundles._.Func._.Eq₁.partialSetoid
d_partialSetoid_740 ::
  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 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_740 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_PartialSetoid_10
d_partialSetoid_740 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_PartialSetoid_10
du_partialSetoid_740 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_partialSetoid_740 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_740 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_PartialSetoid_10
du_partialSetoid_740 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) 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
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.Eq₁.refl
d_refl_742 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny
d_refl_742 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
d_refl_742 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> AgdaAny -> AgdaAny
du_refl_742 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_refl_742 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 -> AgdaAny -> AgdaAny
du_refl_742 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> AgdaAny -> AgdaAny
du_refl_742 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) 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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.Eq₁.reflexive
d_reflexive_744 ::
  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 ->
  T_Func_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_744 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_744 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_744 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_reflexive_744 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_744 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_744 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v4))
              AgdaAny
v5))
-- Function.Bundles._.Func._.Eq₁.setoid
d_setoid_746 ::
  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 ->
  T_Func_714 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_746 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_Setoid_44
d_setoid_746 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_Setoid_44
du_setoid_746 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_setoid_746 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_746 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_Setoid_44
du_setoid_746 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2))
-- Function.Bundles._.Func._.Eq₁.sym
d_sym_748 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_748 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_748 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_748 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_sym_748 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_748 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_748 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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
v4))))
-- Function.Bundles._.Func._.Eq₁.trans
d_trans_750 ::
  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 ->
  T_Func_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_750 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_750 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_750 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_trans_750 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_750 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_750 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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
v4))))
-- Function.Bundles._.Func._.Eq₂._≈_
d__'8776'__754 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> ()
d__'8776'__754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__754 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₂._≉_
d__'8777'__756 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> ()
d__'8777'__756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__756 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₂.Carrier
d_Carrier_758 ::
  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 ->
  T_Func_714 -> ()
d_Carrier_758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_Level_18
d_Carrier_758 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₂.isEquivalence
d_isEquivalence_760 ::
  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 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_760 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_IsEquivalence_26
d_isEquivalence_760 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsEquivalence_26
du_isEquivalence_760 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_isEquivalence_760 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_760 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsEquivalence_26
du_isEquivalence_760 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.Func._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_762 ::
  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 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Func_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_762 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_isPartialEquivalence_762 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_762 :: T_Setoid_44
-> T_Setoid_44 -> T_Func_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_762 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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
v4))))
-- Function.Bundles._.Func._.Eq₂.partialSetoid
d_partialSetoid_764 ::
  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 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_PartialSetoid_10
d_partialSetoid_764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_PartialSetoid_10
du_partialSetoid_764 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_partialSetoid_764 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_764 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_PartialSetoid_10
du_partialSetoid_764 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) 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
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.Eq₂.refl
d_refl_766 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny
d_refl_766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
d_refl_766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> AgdaAny -> AgdaAny
du_refl_766 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_refl_766 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 -> AgdaAny -> AgdaAny
du_refl_766 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> AgdaAny -> AgdaAny
du_refl_766 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) 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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.Eq₂.reflexive
d_reflexive_768 ::
  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 ->
  T_Func_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_768 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_reflexive_768 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_768 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_768 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v4))
              AgdaAny
v5))
-- Function.Bundles._.Func._.Eq₂.setoid
d_setoid_770 ::
  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 ->
  T_Func_714 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_770 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> T_Setoid_44
d_setoid_770 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_Setoid_44
du_setoid_770 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_setoid_770 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_770 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_Setoid_44
du_setoid_770 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
      ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2))
-- Function.Bundles._.Func._.Eq₂.sym
d_sym_772 ::
  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 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_772 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_sym_772 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_772 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_772 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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
v4))))
-- Function.Bundles._.Func._.Eq₂.trans
d_trans_774 ::
  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 ->
  T_Func_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_774 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_714
v6
du_trans_774 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_774 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_774 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_714
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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
v4))))
-- Function.Bundles._.Injection
d_Injection_776 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Injection_776 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Injection_776
  = C_Injection'46'constructor_8675 (AgdaAny -> AgdaAny)
                                    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Injection.to
d_to_784 :: T_Injection_776 -> AgdaAny -> AgdaAny
d_to_784 :: T_Injection_776 -> AgdaAny -> AgdaAny
d_to_784 T_Injection_776
v0
  = case T_Injection_776 -> T_Injection_776
forall a b. a -> b
coe T_Injection_776
v0 of
      C_Injection'46'constructor_8675 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Injection_776
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.cong
d_cong_786 ::
  T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_786 :: T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_786 T_Injection_776
v0
  = case T_Injection_776 -> T_Injection_776
forall a b. a -> b
coe T_Injection_776
v0 of
      C_Injection'46'constructor_8675 AgdaAny -> AgdaAny
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_Injection_776
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.injective
d_injective_788 ::
  T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_788 :: T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_788 T_Injection_776
v0
  = case T_Injection_776 -> T_Injection_776
forall a b. a -> b
coe T_Injection_776
v0 of
      C_Injection'46'constructor_8675 AgdaAny -> AgdaAny
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_Injection_776
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.function
d_function_790 ::
  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 ->
  T_Injection_776 -> T_Func_714
d_function_790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_Func_714
d_function_790 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Injection_776
v6 = T_Injection_776 -> T_Func_714
du_function_790 T_Injection_776
v6
du_function_790 :: T_Injection_776 -> T_Func_714
du_function_790 :: T_Injection_776 -> T_Func_714
du_function_790 T_Injection_776
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714)
-> AgdaAny -> AgdaAny -> T_Func_714
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714
C_Func'46'constructor_6307 ((T_Injection_776 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_776 -> AgdaAny -> AgdaAny
d_to_784 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v0))
      ((T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_786 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v0))
-- Function.Bundles._.Injection._.isCongruent
d_isCongruent_794 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_794 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_IsCongruent_22
d_isCongruent_794 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsCongruent_22
du_isCongruent_794 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_isCongruent_794 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_794 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsCongruent_22
du_isCongruent_794 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) ((T_Injection_776 -> T_Func_714) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2))
-- Function.Bundles._.Injection._.Eq₁._≈_
d__'8776'__798 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> ()
d__'8776'__798 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__798 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁._≉_
d__'8777'__800 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> ()
d__'8777'__800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__800 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁.Carrier
d_Carrier_802 ::
  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 ->
  T_Injection_776 -> ()
d_Carrier_802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_Level_18
d_Carrier_802 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁.isEquivalence
d_isEquivalence_804 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_804 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_IsEquivalence_26
d_isEquivalence_804 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsEquivalence_26
du_isEquivalence_804 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_isEquivalence_804 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_804 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsEquivalence_26
du_isEquivalence_804 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Injection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_806 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Injection_776 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_806 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_isPartialEquivalence_806 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_806 :: T_Setoid_44
-> T_Setoid_44 -> T_Injection_776 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_806 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5)))))
-- Function.Bundles._.Injection._.Eq₁.partialSetoid
d_partialSetoid_808 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_PartialSetoid_10
d_partialSetoid_808 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_PartialSetoid_10
du_partialSetoid_808 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_partialSetoid_808 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_808 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_PartialSetoid_10
du_partialSetoid_808 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₁.refl
d_refl_810 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny
d_refl_810 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
d_refl_810 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> AgdaAny -> AgdaAny
du_refl_810 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_refl_810 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 -> AgdaAny -> AgdaAny
du_refl_810 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> AgdaAny -> AgdaAny
du_refl_810 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₁.reflexive
d_reflexive_812 ::
  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 ->
  T_Injection_776 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_812 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_812 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_reflexive_812 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_812 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_812 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Injection._.Eq₁.setoid
d_setoid_814 ::
  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 ->
  T_Injection_776 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_814 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_Setoid_44
d_setoid_814 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_Setoid_44
du_setoid_814 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_setoid_814 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_814 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_Setoid_44
du_setoid_814 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Injection._.Eq₁.sym
d_sym_816 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_816 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_816 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_sym_816 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_816 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_816 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Injection._.Eq₁.trans
d_trans_818 ::
  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 ->
  T_Injection_776 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_818 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_818 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_trans_818 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_818 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_818 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Injection._.Eq₂._≈_
d__'8776'__822 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> ()
d__'8776'__822 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__822 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂._≉_
d__'8777'__824 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> ()
d__'8777'__824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__824 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂.Carrier
d_Carrier_826 ::
  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 ->
  T_Injection_776 -> ()
d_Carrier_826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_Level_18
d_Carrier_826 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂.isEquivalence
d_isEquivalence_828 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_828 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_IsEquivalence_26
d_isEquivalence_828 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsEquivalence_26
du_isEquivalence_828 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_isEquivalence_828 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_828 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsEquivalence_26
du_isEquivalence_828 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Injection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_830 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Injection_776 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_830 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_isPartialEquivalence_830 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_830 :: T_Setoid_44
-> T_Setoid_44 -> T_Injection_776 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_830 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5)))))
-- Function.Bundles._.Injection._.Eq₂.partialSetoid
d_partialSetoid_832 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_PartialSetoid_10
d_partialSetoid_832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_PartialSetoid_10
du_partialSetoid_832 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_partialSetoid_832 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_832 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_PartialSetoid_10
du_partialSetoid_832 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₂.refl
d_refl_834 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny
d_refl_834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
d_refl_834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> AgdaAny -> AgdaAny
du_refl_834 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_refl_834 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 -> AgdaAny -> AgdaAny
du_refl_834 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> AgdaAny -> AgdaAny
du_refl_834 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₂.reflexive
d_reflexive_836 ::
  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 ->
  T_Injection_776 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_836 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_836 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_reflexive_836 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_836 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_836 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Injection._.Eq₂.setoid
d_setoid_838 ::
  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 ->
  T_Injection_776 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_Setoid_44
d_setoid_838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_Setoid_44
du_setoid_838 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_setoid_838 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_838 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_Setoid_44
du_setoid_838 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Injection._.Eq₂.sym
d_sym_840 ::
  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 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_840 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_sym_840 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_840 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_840 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Injection._.Eq₂.trans
d_trans_842 ::
  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 ->
  T_Injection_776 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_842 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_trans_842 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_842 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_842 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = let v3 :: t
v3 = (T_Injection_776 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Injection.isInjection
d_isInjection_844 ::
  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 ->
  T_Injection_776 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
d_isInjection_844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_776
-> T_IsInjection_92
d_isInjection_844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsInjection_92
du_isInjection_844 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_776
v6
du_isInjection_844 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_776 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
du_isInjection_844 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsInjection_92
du_isInjection_844 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_776
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInjection_92)
-> AgdaAny -> AgdaAny -> T_IsInjection_92
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInjection_92
MAlonzo.Code.Function.Structures.C_IsInjection'46'constructor_3997
      ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
         ((T_Injection_776 -> T_Func_714) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_776 -> T_Func_714
du_function_790 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2)))
      ((T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_776 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_788 (T_Injection_776 -> AgdaAny
forall a b. a -> b
coe T_Injection_776
v2))
-- Function.Bundles._.Surjection
d_Surjection_846 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Surjection_846 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Surjection_846
  = C_Surjection'46'constructor_11197 (AgdaAny -> AgdaAny)
                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Bundles._.Surjection.to
d_to_854 :: T_Surjection_846 -> AgdaAny -> AgdaAny
d_to_854 :: T_Surjection_846 -> AgdaAny -> AgdaAny
d_to_854 T_Surjection_846
v0
  = case T_Surjection_846 -> T_Surjection_846
forall a b. a -> b
coe T_Surjection_846
v0 of
      C_Surjection'46'constructor_11197 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Surjection_846
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.cong
d_cong_856 ::
  T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_856 :: T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_856 T_Surjection_846
v0
  = case T_Surjection_846 -> T_Surjection_846
forall a b. a -> b
coe T_Surjection_846
v0 of
      C_Surjection'46'constructor_11197 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_Surjection_846
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.surjective
d_surjective_858 ::
  T_Surjection_846 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_858 :: T_Surjection_846 -> AgdaAny -> T_Σ_14
d_surjective_858 T_Surjection_846
v0
  = case T_Surjection_846 -> T_Surjection_846
forall a b. a -> b
coe T_Surjection_846
v0 of
      C_Surjection'46'constructor_11197 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v3
      T_Surjection_846
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.function
d_function_860 ::
  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 ->
  T_Surjection_846 -> T_Func_714
d_function_860 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_Func_714
d_function_860 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Surjection_846
v6 = T_Surjection_846 -> T_Func_714
du_function_860 T_Surjection_846
v6
du_function_860 :: T_Surjection_846 -> T_Func_714
du_function_860 :: T_Surjection_846 -> T_Func_714
du_function_860 T_Surjection_846
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714)
-> AgdaAny -> AgdaAny -> T_Func_714
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714
C_Func'46'constructor_6307 ((T_Surjection_846 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_846 -> AgdaAny -> AgdaAny
d_to_854 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v0))
      ((T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_856 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v0))
-- Function.Bundles._.Surjection._.isCongruent
d_isCongruent_864 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_IsCongruent_22
d_isCongruent_864 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> T_IsCongruent_22
du_isCongruent_864 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_isCongruent_864 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_864 :: T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> T_IsCongruent_22
du_isCongruent_864 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) ((T_Surjection_846 -> T_Func_714) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2))
-- Function.Bundles._.Surjection._.Eq₁._≈_
d__'8776'__868 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> ()
d__'8776'__868 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__868 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁._≉_
d__'8777'__870 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> ()
d__'8777'__870 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__870 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁.Carrier
d_Carrier_872 ::
  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 ->
  T_Surjection_846 -> ()
d_Carrier_872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_Level_18
d_Carrier_872 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁.isEquivalence
d_isEquivalence_874 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_IsEquivalence_26
d_isEquivalence_874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsEquivalence_26
du_isEquivalence_874 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_isEquivalence_874 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_874 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsEquivalence_26
du_isEquivalence_874 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Surjection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_876 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_876 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_isPartialEquivalence_876 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_876 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_876 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5)))))
-- Function.Bundles._.Surjection._.Eq₁.partialSetoid
d_partialSetoid_878 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_PartialSetoid_10
d_partialSetoid_878 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_PartialSetoid_10
du_partialSetoid_878 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_partialSetoid_878 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_878 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_PartialSetoid_10
du_partialSetoid_878 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Surjection._.Eq₁.refl
d_refl_880 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny
d_refl_880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
d_refl_880 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> AgdaAny
du_refl_880 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_refl_880 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny
du_refl_880 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> AgdaAny
du_refl_880 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Surjection._.Eq₁.reflexive
d_reflexive_882 ::
  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 ->
  T_Surjection_846 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_882 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_882 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_reflexive_882 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_882 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_882 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Surjection._.Eq₁.setoid
d_setoid_884 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_Setoid_44
d_setoid_884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> T_Setoid_44
du_setoid_884 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_setoid_884 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_884 :: T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> T_Setoid_44
du_setoid_884 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₁.sym
d_sym_886 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_886 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_sym_886 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_886 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_886 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Surjection._.Eq₁.trans
d_trans_888 ::
  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 ->
  T_Surjection_846 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_888 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_888 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_trans_888 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_888 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_888 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Surjection._.Eq₂._≈_
d__'8776'__892 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> ()
d__'8776'__892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__892 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂._≉_
d__'8777'__894 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> ()
d__'8777'__894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__894 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂.Carrier
d_Carrier_896 ::
  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 ->
  T_Surjection_846 -> ()
d_Carrier_896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_Level_18
d_Carrier_896 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂.isEquivalence
d_isEquivalence_898 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_IsEquivalence_26
d_isEquivalence_898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsEquivalence_26
du_isEquivalence_898 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_isEquivalence_898 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_898 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsEquivalence_26
du_isEquivalence_898 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Surjection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_900 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_900 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_900 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_isPartialEquivalence_900 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_900 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_900 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5)))))
-- Function.Bundles._.Surjection._.Eq₂.partialSetoid
d_partialSetoid_902 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_PartialSetoid_10
d_partialSetoid_902 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_PartialSetoid_10
du_partialSetoid_902 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_partialSetoid_902 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_902 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_PartialSetoid_10
du_partialSetoid_902 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Surjection._.Eq₂.refl
d_refl_904 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny
d_refl_904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
d_refl_904 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> AgdaAny
du_refl_904 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_refl_904 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny
du_refl_904 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> AgdaAny
du_refl_904 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Surjection._.Eq₂.reflexive
d_reflexive_906 ::
  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 ->
  T_Surjection_846 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_906 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_906 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_reflexive_906 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_906 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_906 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Surjection._.Eq₂.setoid
d_setoid_908 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_Setoid_44
d_setoid_908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> T_Setoid_44
du_setoid_908 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_setoid_908 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_908 :: T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> T_Setoid_44
du_setoid_908 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₂.sym
d_sym_910 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_910 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_910 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_sym_910 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_910 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_910 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Surjection._.Eq₂.trans
d_trans_912 ::
  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 ->
  T_Surjection_846 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_912 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_912 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_trans_912 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_912 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_912 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = let v3 :: t
v3 = (T_Surjection_846 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Surjection.isSurjection
d_isSurjection_914 ::
  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 ->
  T_Surjection_846 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
d_isSurjection_914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> T_IsSurjection_162
d_isSurjection_914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162
du_isSurjection_914 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_isSurjection_914 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
du_isSurjection_914 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162
du_isSurjection_914 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = (T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162
MAlonzo.Code.Function.Structures.C_IsSurjection'46'constructor_6463
      ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
         ((T_Surjection_846 -> T_Func_714) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_846 -> T_Func_714
du_function_860 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2)))
      ((T_Surjection_846 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_846 -> AgdaAny -> T_Σ_14
d_surjective_858 (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2))
-- Function.Bundles._.Surjection._.strictlySurjective
d_strictlySurjective_918 ::
  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 ->
  T_Surjection_846 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> T_Σ_14
du_strictlySurjective_918 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6
du_strictlySurjective_918 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_918 :: T_Setoid_44 -> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> T_Σ_14
du_strictlySurjective_918 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2
  = (T_IsSurjection_162 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSurjection_162 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_230
      ((T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162
du_isSurjection_914 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2))
-- Function.Bundles._.Surjection.to⁻
d_to'8315'_920 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny
d_to'8315'_920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
d_to'8315'_920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Surjection_846
v6 AgdaAny
v7
  = T_Surjection_846 -> AgdaAny -> AgdaAny
du_to'8315'_920 T_Surjection_846
v6 AgdaAny
v7
du_to'8315'_920 :: T_Surjection_846 -> AgdaAny -> AgdaAny
du_to'8315'_920 :: T_Surjection_846 -> AgdaAny -> AgdaAny
du_to'8315'_920 T_Surjection_846
v0 AgdaAny
v1
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_Surjection_846 -> AgdaAny -> T_Σ_14)
-> T_Surjection_846 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_846 -> AgdaAny -> T_Σ_14
d_surjective_858 T_Surjection_846
v0 AgdaAny
v1)
-- Function.Bundles._.Surjection.to∘to⁻
d_to'8728'to'8315'_924 ::
  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 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny
d_to'8728'to'8315'_924 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_846
-> AgdaAny
-> AgdaAny
d_to'8728'to'8315'_924 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 AgdaAny
v7
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> AgdaAny
du_to'8728'to'8315'_924 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_846
v6 AgdaAny
v7
du_to'8728'to'8315'_924 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_846 -> AgdaAny -> AgdaAny
du_to'8728'to'8315'_924 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> AgdaAny -> AgdaAny
du_to'8728'to'8315'_924 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_846
v2 AgdaAny
v3
  = (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_IsSurjection_162 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSurjection_162 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_230
         ((T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162
du_isSurjection_914 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_846 -> AgdaAny
forall a b. a -> b
coe T_Surjection_846
v2)) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
-- Function.Bundles._.Bijection
d_Bijection_926 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Bijection_926 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Bijection_926
  = C_Bijection'46'constructor_15277 (AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Function.Bundles._.Bijection.to
d_to_934 :: T_Bijection_926 -> AgdaAny -> AgdaAny
d_to_934 :: T_Bijection_926 -> AgdaAny -> AgdaAny
d_to_934 T_Bijection_926
v0
  = case T_Bijection_926 -> T_Bijection_926
forall a b. a -> b
coe T_Bijection_926
v0 of
      C_Bijection'46'constructor_15277 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Bijection_926
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.cong
d_cong_936 ::
  T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_936 :: T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_936 T_Bijection_926
v0
  = case T_Bijection_926 -> T_Bijection_926
forall a b. a -> b
coe T_Bijection_926
v0 of
      C_Bijection'46'constructor_15277 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_Bijection_926
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.bijective
d_bijective_938 ::
  T_Bijection_926 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_bijective_938 :: T_Bijection_926 -> T_Σ_14
d_bijective_938 T_Bijection_926
v0
  = case T_Bijection_926 -> T_Bijection_926
forall a b. a -> b
coe T_Bijection_926
v0 of
      C_Bijection'46'constructor_15277 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_Bijection_926
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.injective
d_injective_940 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_injective_940 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_926
v6 AgdaAny
v7 AgdaAny
v8
  = T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_940 T_Bijection_926
v6 AgdaAny
v7 AgdaAny
v8
du_injective_940 ::
  T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_940 :: T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_940 T_Bijection_926
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny)
-> 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_Bijection_926 -> T_Σ_14
d_bijective_938 (T_Bijection_926 -> T_Bijection_926
forall a b. a -> b
coe T_Bijection_926
v0))
      AgdaAny
v1 AgdaAny
v2
-- Function.Bundles._.Bijection.surjective
d_surjective_942 ::
  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 ->
  T_Bijection_926 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_942 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> T_Σ_14
d_surjective_942 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_926
v6 = T_Bijection_926 -> AgdaAny -> T_Σ_14
du_surjective_942 T_Bijection_926
v6
du_surjective_942 ::
  T_Bijection_926 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_surjective_942 :: T_Bijection_926 -> AgdaAny -> T_Σ_14
du_surjective_942 T_Bijection_926
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_Bijection_926 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> T_Σ_14
d_bijective_938 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0))
-- Function.Bundles._.Bijection.injection
d_injection_944 ::
  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 ->
  T_Bijection_926 -> T_Injection_776
d_injection_944 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Injection_776
d_injection_944 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_926
v6 = T_Bijection_926 -> T_Injection_776
du_injection_944 T_Bijection_926
v6
du_injection_944 :: T_Bijection_926 -> T_Injection_776
du_injection_944 :: T_Bijection_926 -> T_Injection_776
du_injection_944 T_Bijection_926
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Injection_776)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Injection_776
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Injection_776
C_Injection'46'constructor_8675 ((T_Bijection_926 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> AgdaAny -> AgdaAny
d_to_934 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0))
      ((T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_936 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0)) ((T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_940 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0))
-- Function.Bundles._.Bijection.surjection
d_surjection_946 ::
  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 ->
  T_Bijection_926 -> T_Surjection_846
d_surjection_946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Surjection_846
d_surjection_946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_926
v6 = T_Bijection_926 -> T_Surjection_846
du_surjection_946 T_Bijection_926
v6
du_surjection_946 :: T_Bijection_926 -> T_Surjection_846
du_surjection_946 :: T_Bijection_926 -> T_Surjection_846
du_surjection_946 T_Bijection_926
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_846)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_846
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_846
C_Surjection'46'constructor_11197 ((T_Bijection_926 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> AgdaAny -> AgdaAny
d_to_934 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0))
      ((T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_936 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0)) ((T_Bijection_926 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> AgdaAny -> T_Σ_14
du_surjective_942 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0))
-- Function.Bundles._.Bijection._.isInjection
d_isInjection_950 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
d_isInjection_950 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_IsInjection_92
d_isInjection_950 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsInjection_92
du_isInjection_950 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_isInjection_950 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
du_isInjection_950 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsInjection_92
du_isInjection_950 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = (T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsInjection_92)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsInjection_92
forall a b. a -> b
coe
      T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsInjection_92
du_isInjection_844 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Bijection_926 -> T_Injection_776) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> T_Injection_776
du_injection_944 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2))
-- Function.Bundles._.Bijection._.isSurjection
d_isSurjection_954 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
d_isSurjection_954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_IsSurjection_162
d_isSurjection_954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsSurjection_162
du_isSurjection_954 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_isSurjection_954 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
du_isSurjection_954 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsSurjection_162
du_isSurjection_954 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162
du_isSurjection_914 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Bijection_926 -> T_Surjection_846) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> T_Surjection_846
du_surjection_946 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2))
-- Function.Bundles._.Bijection._.strictlySurjective
d_strictlySurjective_956 ::
  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 ->
  T_Bijection_926 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_956 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_956 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> AgdaAny -> T_Σ_14
du_strictlySurjective_956 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_strictlySurjective_956 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_956 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> AgdaAny -> T_Σ_14
du_strictlySurjective_956 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Bijection_926 -> T_Surjection_846) -> AgdaAny -> t
forall a b. a -> b
coe T_Bijection_926 -> T_Surjection_846
du_surjection_946 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsSurjection_162 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSurjection_162 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_230
         ((T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_Surjection_846 -> T_IsSurjection_162
du_isSurjection_914 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Bijection._.to⁻
d_to'8315'_958 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny
d_to'8315'_958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
d_to'8315'_958 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_926
v6 = T_Bijection_926 -> AgdaAny -> AgdaAny
du_to'8315'_958 T_Bijection_926
v6
du_to'8315'_958 :: T_Bijection_926 -> AgdaAny -> AgdaAny
du_to'8315'_958 :: T_Bijection_926 -> AgdaAny -> AgdaAny
du_to'8315'_958 T_Bijection_926
v0
  = (T_Surjection_846 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_846 -> AgdaAny -> AgdaAny
du_to'8315'_920 ((T_Bijection_926 -> T_Surjection_846) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> T_Surjection_846
du_surjection_946 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v0))
-- Function.Bundles._.Bijection.isBijection
d_isBijection_960 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238
d_isBijection_960 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_IsBijection_238
d_isBijection_960 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_isBijection_960 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Function.Structures.T_IsBijection_238
du_isBijection_960 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = (T_IsInjection_92 -> (AgdaAny -> T_Σ_14) -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe
      T_IsInjection_92 -> (AgdaAny -> T_Σ_14) -> T_IsBijection_238
MAlonzo.Code.Function.Structures.C_IsBijection'46'constructor_10113
      ((T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsInjection_92)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_Setoid_44 -> T_Injection_776 -> T_IsInjection_92
du_isInjection_844 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
         ((T_Bijection_926 -> T_Injection_776) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> T_Injection_776
du_injection_944 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2)))
      ((T_Bijection_926 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_926 -> AgdaAny -> T_Σ_14
du_surjective_942 (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2))
-- Function.Bundles._.Bijection._.Eq₁._≈_
d__'8776'__966 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> ()
d__'8776'__966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__966 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁._≉_
d__'8777'__968 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> ()
d__'8777'__968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__968 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁.Carrier
d_Carrier_970 ::
  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 ->
  T_Bijection_926 -> ()
d_Carrier_970 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Level_18
d_Carrier_970 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁.isEquivalence
d_isEquivalence_972 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_972 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_IsEquivalence_26
d_isEquivalence_972 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsEquivalence_26
du_isEquivalence_972 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_isEquivalence_972 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_972 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsEquivalence_26
du_isEquivalence_972 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Bijection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_974 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_974 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Bijection_926 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_974 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_isPartialEquivalence_974 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_974 :: T_Setoid_44
-> T_Setoid_44 -> T_Bijection_926 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_974 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))))))
-- Function.Bundles._.Bijection._.Eq₁.partialSetoid
d_partialSetoid_976 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_PartialSetoid_10
d_partialSetoid_976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_PartialSetoid_10
du_partialSetoid_976 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_partialSetoid_976 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_976 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_PartialSetoid_10
du_partialSetoid_976 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
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
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₁.refl
d_refl_978 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny
d_refl_978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
d_refl_978 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> AgdaAny -> AgdaAny
du_refl_978 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_refl_978 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny
du_refl_978 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> AgdaAny -> AgdaAny
du_refl_978 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₁.reflexive
d_reflexive_980 ::
  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 ->
  T_Bijection_926 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_980 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_reflexive_980 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_980 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_980 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Bijection._.Eq₁.setoid
d_setoid_982 ::
  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 ->
  T_Bijection_926 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Setoid_44
d_setoid_982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_Setoid_44
du_setoid_982 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_setoid_982 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_982 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_Setoid_44
du_setoid_982 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
            ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v4))))
-- Function.Bundles._.Bijection._.Eq₁.sym
d_sym_984 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_984 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_sym_984 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_984 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_984 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._.Bijection._.Eq₁.trans
d_trans_986 ::
  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 ->
  T_Bijection_926 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_986 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_trans_986 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_986 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_986 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._.Bijection._.Eq₂._≈_
d__'8776'__990 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> ()
d__'8776'__990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__990 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂._≉_
d__'8777'__992 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> ()
d__'8777'__992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__992 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂.Carrier
d_Carrier_994 ::
  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 ->
  T_Bijection_926 -> ()
d_Carrier_994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Level_18
d_Carrier_994 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂.isEquivalence
d_isEquivalence_996 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_IsEquivalence_26
d_isEquivalence_996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsEquivalence_26
du_isEquivalence_996 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_isEquivalence_996 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_996 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsEquivalence_26
du_isEquivalence_996 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Bijection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_998 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Bijection_926 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_998 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_isPartialEquivalence_998 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_998 :: T_Setoid_44
-> T_Setoid_44 -> T_Bijection_926 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_998 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))))))
-- Function.Bundles._.Bijection._.Eq₂.partialSetoid
d_partialSetoid_1000 ::
  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 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_PartialSetoid_10
d_partialSetoid_1000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_PartialSetoid_10
du_partialSetoid_1000 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_partialSetoid_1000 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1000 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_PartialSetoid_10
du_partialSetoid_1000 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
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
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₂.refl
d_refl_1002 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny
d_refl_1002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
d_refl_1002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> AgdaAny -> AgdaAny
du_refl_1002 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_refl_1002 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny
du_refl_1002 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> AgdaAny -> AgdaAny
du_refl_1002 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₂.reflexive
d_reflexive_1004 ::
  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 ->
  T_Bijection_926 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1004 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1004 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_reflexive_1004 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1004 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1004 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Bijection._.Eq₂.setoid
d_setoid_1006 ::
  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 ->
  T_Bijection_926 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> T_Setoid_44
d_setoid_1006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_Setoid_44
du_setoid_1006 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_setoid_1006 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1006 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_Setoid_44
du_setoid_1006 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
            ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v4))))
-- Function.Bundles._.Bijection._.Eq₂.sym
d_sym_1008 ::
  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 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1008 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1008 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_sym_1008 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1008 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1008 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._.Bijection._.Eq₂.trans
d_trans_1010 ::
  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 ->
  T_Bijection_926 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1010 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_926
v6
du_trans_1010 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_926 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1010 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_926
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1010 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_926
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_926 -> T_IsBijection_238
du_isBijection_960 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_926 -> AgdaAny
forall a b. a -> b
coe T_Bijection_926
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_238 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_246 (AgdaAny -> T_IsBijection_238
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._._._≈_
d__'8776'__1030 ::
  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'__1030 :: 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'__1030 = 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.Bundles._._.Carrier
d_Carrier_1032 ::
  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_1032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
d_Carrier_1032 = 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.Bundles._._.IsBiInverse
d_IsBiInverse_1044 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBiInverse_1044 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
-- Function.Bundles._._.IsCongruent
d_IsCongruent_1048 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCongruent_1048 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsInverse
d_IsInverse_1052 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInverse_1052 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsLeftInverse
d_IsLeftInverse_1054 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLeftInverse_1054 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsRightInverse
d_IsRightInverse_1056 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRightInverse_1056 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsSplitSurjection
d_IsSplitSurjection_1058 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSplitSurjection_1058 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsBiInverse.from₁-cong
d_from'8321''45'cong_1126 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_1126 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_1126 T_IsBiInverse_666
v0
  = (T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'8321''45'cong_686 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0)
-- Function.Bundles._._.IsBiInverse.from₂-cong
d_from'8322''45'cong_1128 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_1128 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_1128 T_IsBiInverse_666
v0
  = (T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'8322''45'cong_688 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0)
-- Function.Bundles._._.IsBiInverse.inverseʳ
d_inverse'691'_1130 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1130 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1130 T_IsBiInverse_666
v0
  = (T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'691'_692 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0)
-- Function.Bundles._._.IsBiInverse.inverseˡ
d_inverse'737'_1132 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1132 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1132 T_IsBiInverse_666
v0
  = (T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'737'_690 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0)
-- Function.Bundles._._.IsBiInverse.to-isCongruent
d_to'45'isCongruent_1140 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_666 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_to'45'isCongruent_1140 :: T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_1140 T_IsBiInverse_666
v0
  = (T_IsBiInverse_666 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_IsBiInverse_666 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_to'45'isCongruent_684 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0)
-- Function.Bundles._._.IsCongruent.cong
d_cong_1262 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1262 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1262 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_cong_32 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.isEquivalence₁
d_isEquivalence'8321'_1264 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_1264 :: T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_1264 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.isEquivalence₂
d_isEquivalence'8322'_1266 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_1266 :: T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_1266 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsInverse.inverseʳ
d_inverse'691'_1382 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1382 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1382 T_IsInverse_490
v0
  = (T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'691'_502 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)
-- Function.Bundles._._.IsInverse.isLeftInverse
d_isLeftInverse_1392 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
d_isLeftInverse_1392 :: T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_1392 T_IsInverse_490
v0
  = (T_IsInverse_490 -> T_IsLeftInverse_322)
-> AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)
-- Function.Bundles._._.IsInverse.Eq₁._≈_
d__'8776'__1406 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1406 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1406 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁._≉_
d__'8777'__1408 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1408 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1408 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁.Carrier
d_Carrier_1410 ::
  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.Function.Structures.T_IsInverse_490 -> ()
d_Carrier_1410 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Level_18
d_Carrier_1410 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁.isEquivalence
d_isEquivalence_1412 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsEquivalence_26
d_isEquivalence_1412 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_1412 T_IsInverse_490
v8
du_isEquivalence_1412 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1412 :: T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_1412 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsInverse.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1414 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1414 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1414 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1414 T_IsInverse_490
v8
du_isPartialEquivalence_1414 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1414 :: T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1414 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3)))))
-- Function.Bundles._._.IsInverse.Eq₁.partialSetoid
d_partialSetoid_1416 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_PartialSetoid_10
d_partialSetoid_1416 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_1416 T_IsInverse_490
v8
du_partialSetoid_1416 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1416 :: T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_1416 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₁.refl
d_refl_1418 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny
d_refl_1418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
d_refl_1418 ~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_IsInverse_490
v8 = T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_1418 T_IsInverse_490
v8
du_refl_1418 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny
du_refl_1418 :: T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_1418 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₁.reflexive
d_reflexive_1420 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1420 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1420 T_IsInverse_490
v8
du_reflexive_1420 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1420 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1420 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsInverse.Eq₁.setoid
d_setoid_1422 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Setoid_44
d_setoid_1422 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_Setoid_44
du_setoid_1422 T_IsInverse_490
v8
du_setoid_1422 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1422 :: T_IsInverse_490 -> T_Setoid_44
du_setoid_1422 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1)))
-- Function.Bundles._._.IsInverse.Eq₁.sym
d_sym_1424 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1424 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1424 ~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_IsInverse_490
v8 = T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1424 T_IsInverse_490
v8
du_sym_1424 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1424 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1424 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsInverse.Eq₁.trans
d_trans_1426 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1426 ~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_IsInverse_490
v8 = T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1426 T_IsInverse_490
v8
du_trans_1426 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1426 :: T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1426 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsInverse.Eq₂._≈_
d__'8776'__1430 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1430 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂._≉_
d__'8777'__1432 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1432 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂.Carrier
d_Carrier_1434 ::
  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.Function.Structures.T_IsInverse_490 -> ()
d_Carrier_1434 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Level_18
d_Carrier_1434 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂.isEquivalence
d_isEquivalence_1436 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1436 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsEquivalence_26
d_isEquivalence_1436 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_1436 T_IsInverse_490
v8
du_isEquivalence_1436 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1436 :: T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_1436 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsInverse.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1438 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1438 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1438 T_IsInverse_490
v8
du_isPartialEquivalence_1438 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1438 :: T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1438 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3)))))
-- Function.Bundles._._.IsInverse.Eq₂.partialSetoid
d_partialSetoid_1440 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_PartialSetoid_10
d_partialSetoid_1440 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_1440 T_IsInverse_490
v8
du_partialSetoid_1440 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1440 :: T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_1440 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₂.refl
d_refl_1442 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny
d_refl_1442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
d_refl_1442 ~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_IsInverse_490
v8 = T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_1442 T_IsInverse_490
v8
du_refl_1442 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny
du_refl_1442 :: T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_1442 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₂.reflexive
d_reflexive_1444 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1444 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1444 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1444 T_IsInverse_490
v8
du_reflexive_1444 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1444 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1444 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsInverse.Eq₂.setoid
d_setoid_1446 ::
  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.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1446 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Setoid_44
d_setoid_1446 ~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_IsInverse_490
v8
  = T_IsInverse_490 -> T_Setoid_44
du_setoid_1446 T_IsInverse_490
v8
du_setoid_1446 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1446 :: T_IsInverse_490 -> T_Setoid_44
du_setoid_1446 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1)))
-- Function.Bundles._._.IsInverse.Eq₂.sym
d_sym_1448 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1448 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1448 ~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_IsInverse_490
v8 = T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1448 T_IsInverse_490
v8
du_sym_1448 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1448 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1448 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsInverse.Eq₂.trans
d_trans_1450 ::
  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.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1450 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1450 ~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_IsInverse_490
v8 = T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1450 T_IsInverse_490
v8
du_trans_1450 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1450 :: T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1450 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1
          = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) 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
v3)))))
-- Function.Bundles._._.IsLeftInverse.from-cong
d_from'45'cong_1454 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1454 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1454 T_IsLeftInverse_322
v0
  = (T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'45'cong_336 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0)
-- Function.Bundles._._.IsLeftInverse.inverseˡ
d_inverse'737'_1456 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1456 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1456 T_IsLeftInverse_322
v0
  = (T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'737'_338 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0)
-- Function.Bundles._._.IsLeftInverse.isCongruent
d_isCongruent_1458 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1458 :: T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_1458 T_IsLeftInverse_322
v0
  = (T_IsLeftInverse_322 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0)
-- Function.Bundles._._.IsLeftInverse.isSurjection
d_isSurjection_1464 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
d_isSurjection_1464 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsSurjection_162
d_isSurjection_1464 ~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)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsSurjection_162
du_isSurjection_1464
du_isSurjection_1464 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
du_isSurjection_1464 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsSurjection_162
du_isSurjection_1464 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_322
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsSurjection_162
forall a b. a -> b
coe (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
MAlonzo.Code.Function.Structures.du_isSurjection_400 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_322
v2
-- Function.Bundles._._.IsLeftInverse.strictlyInverseˡ
d_strictlyInverse'737'_1466 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny
d_strictlyInverse'737'_1466 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_1466 ~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)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
du_strictlyInverse'737'_1466
du_strictlyInverse'737'_1466 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny
du_strictlyInverse'737'_1466 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
du_strictlyInverse'737'_1466 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_322
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_396 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_322
v2
      AgdaAny
v3
-- Function.Bundles._._.IsLeftInverse.Eq₁._≈_
d__'8776'__1472 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1472 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1472 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₁._≉_
d__'8777'__1474 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1474 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1474 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₁.Carrier
d_Carrier_1476 ::
  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.Function.Structures.T_IsLeftInverse_322 -> ()
d_Carrier_1476 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Level_18
d_Carrier_1476 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₁.isEquivalence
d_isEquivalence_1478 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1478 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsEquivalence_26
d_isEquivalence_1478 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_1478 T_IsLeftInverse_322
v8
du_isEquivalence_1478 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1478 :: T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_1478 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Bundles._._.IsLeftInverse.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1480 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1480 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1480 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1480 T_IsLeftInverse_322
v8
du_isPartialEquivalence_1480 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1480 :: T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1480 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))))
-- Function.Bundles._._.IsLeftInverse.Eq₁.partialSetoid
d_partialSetoid_1482 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1482 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_PartialSetoid_10
d_partialSetoid_1482 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_1482 T_IsLeftInverse_322
v8
du_partialSetoid_1482 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1482 :: T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_1482 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
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
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsLeftInverse.Eq₁.refl
d_refl_1484 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny
d_refl_1484 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
d_refl_1484 ~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_IsLeftInverse_322
v8 = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_1484 T_IsLeftInverse_322
v8
du_refl_1484 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny
du_refl_1484 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_1484 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsLeftInverse.Eq₁.reflexive
d_reflexive_1486 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1486 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1486 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1486 T_IsLeftInverse_322
v8
du_reflexive_1486 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1486 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1486 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))
-- Function.Bundles._._.IsLeftInverse.Eq₁.setoid
d_setoid_1488 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1488 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Setoid_44
d_setoid_1488 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_1488 T_IsLeftInverse_322
v8
du_setoid_1488 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1488 :: T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_1488 T_IsLeftInverse_322
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0))
-- Function.Bundles._._.IsLeftInverse.Eq₁.sym
d_sym_1490 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1490 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1490 ~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_IsLeftInverse_322
v8 = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1490 T_IsLeftInverse_322
v8
du_sym_1490 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1490 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1490 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsLeftInverse.Eq₁.trans
d_trans_1492 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1492 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1492 ~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_IsLeftInverse_322
v8 = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1492 T_IsLeftInverse_322
v8
du_trans_1492 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1492 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1492 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsLeftInverse.Eq₂._≈_
d__'8776'__1496 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1496 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1496 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₂._≉_
d__'8777'__1498 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1498 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1498 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₂.Carrier
d_Carrier_1500 ::
  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.Function.Structures.T_IsLeftInverse_322 -> ()
d_Carrier_1500 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Level_18
d_Carrier_1500 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₂.isEquivalence
d_isEquivalence_1502 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1502 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsEquivalence_26
d_isEquivalence_1502 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_1502 T_IsLeftInverse_322
v8
du_isEquivalence_1502 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1502 :: T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_1502 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Bundles._._.IsLeftInverse.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1504 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1504 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1504 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1504 T_IsLeftInverse_322
v8
du_isPartialEquivalence_1504 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1504 :: T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1504 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))))
-- Function.Bundles._._.IsLeftInverse.Eq₂.partialSetoid
d_partialSetoid_1506 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1506 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_PartialSetoid_10
d_partialSetoid_1506 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_1506 T_IsLeftInverse_322
v8
du_partialSetoid_1506 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1506 :: T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_1506 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
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
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsLeftInverse.Eq₂.refl
d_refl_1508 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny
d_refl_1508 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
d_refl_1508 ~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_IsLeftInverse_322
v8 = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_1508 T_IsLeftInverse_322
v8
du_refl_1508 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny
du_refl_1508 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_1508 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsLeftInverse.Eq₂.reflexive
d_reflexive_1510 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1510 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1510 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1510 T_IsLeftInverse_322
v8
du_reflexive_1510 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1510 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1510 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))
-- Function.Bundles._._.IsLeftInverse.Eq₂.setoid
d_setoid_1512 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1512 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Setoid_44
d_setoid_1512 ~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_IsLeftInverse_322
v8
  = T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_1512 T_IsLeftInverse_322
v8
du_setoid_1512 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1512 :: T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_1512 T_IsLeftInverse_322
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0))
-- Function.Bundles._._.IsLeftInverse.Eq₂.sym
d_sym_1514 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1514 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1514 ~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_IsLeftInverse_322
v8 = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1514 T_IsLeftInverse_322
v8
du_sym_1514 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1514 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1514 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsLeftInverse.Eq₂.trans
d_trans_1516 ::
  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.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1516 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1516 ~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_IsLeftInverse_322
v8 = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1516 T_IsLeftInverse_322
v8
du_trans_1516 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1516 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1516 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsRightInverse.from-cong
d_from'45'cong_1520 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1520 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1520 T_IsRightInverse_408
v0
  = (T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'45'cong_422 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0)
-- Function.Bundles._._.IsRightInverse.inverseʳ
d_inverse'691'_1522 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1522 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1522 T_IsRightInverse_408
v0
  = (T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'691'_424 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0)
-- Function.Bundles._._.IsRightInverse.isCongruent
d_isCongruent_1524 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1524 :: T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_1524 T_IsRightInverse_408
v0
  = (T_IsRightInverse_408 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0)
-- Function.Bundles._._.IsRightInverse.strictlyInverseʳ
d_strictlyInverse'691'_1530 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny
d_strictlyInverse'691'_1530 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_1530 ~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)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
du_strictlyInverse'691'_1530
du_strictlyInverse'691'_1530 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny
du_strictlyInverse'691'_1530 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
du_strictlyInverse'691'_1530 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_IsRightInverse_408
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'691'_482 AgdaAny -> AgdaAny
v0 T_IsRightInverse_408
v2
      AgdaAny
v3
-- Function.Bundles._._.IsRightInverse.Eq₁._≈_
d__'8776'__1536 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1536 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1536 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₁._≉_
d__'8777'__1538 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1538 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1538 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₁.Carrier
d_Carrier_1540 ::
  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.Function.Structures.T_IsRightInverse_408 -> ()
d_Carrier_1540 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Level_18
d_Carrier_1540 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₁.isEquivalence
d_isEquivalence_1542 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1542 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsEquivalence_26
d_isEquivalence_1542 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_1542 T_IsRightInverse_408
v8
du_isEquivalence_1542 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1542 :: T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_1542 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Bundles._._.IsRightInverse.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1544 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1544 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1544 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 T_IsRightInverse_408
v8
du_isPartialEquivalence_1544 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 :: T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))))
-- Function.Bundles._._.IsRightInverse.Eq₁.partialSetoid
d_partialSetoid_1546 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1546 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_PartialSetoid_10
d_partialSetoid_1546 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_1546 T_IsRightInverse_408
v8
du_partialSetoid_1546 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1546 :: T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_1546 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
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
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsRightInverse.Eq₁.refl
d_refl_1548 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny
d_refl_1548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
d_refl_1548 ~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_IsRightInverse_408
v8 = T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_1548 T_IsRightInverse_408
v8
du_refl_1548 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny
du_refl_1548 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_1548 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsRightInverse.Eq₁.reflexive
d_reflexive_1550 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1550 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1550 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1550 T_IsRightInverse_408
v8
du_reflexive_1550 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1550 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1550 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))
-- Function.Bundles._._.IsRightInverse.Eq₁.setoid
d_setoid_1552 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1552 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Setoid_44
d_setoid_1552 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_Setoid_44
du_setoid_1552 T_IsRightInverse_408
v8
du_setoid_1552 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1552 :: T_IsRightInverse_408 -> T_Setoid_44
du_setoid_1552 T_IsRightInverse_408
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0))
-- Function.Bundles._._.IsRightInverse.Eq₁.sym
d_sym_1554 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1554 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1554 ~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_IsRightInverse_408
v8 = T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1554 T_IsRightInverse_408
v8
du_sym_1554 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1554 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1554 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsRightInverse.Eq₁.trans
d_trans_1556 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1556 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1556 ~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_IsRightInverse_408
v8 = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1556 T_IsRightInverse_408
v8
du_trans_1556 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1556 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1556 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsRightInverse.Eq₂._≈_
d__'8776'__1560 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1560 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1560 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₂._≉_
d__'8777'__1562 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1562 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1562 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₂.Carrier
d_Carrier_1564 ::
  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.Function.Structures.T_IsRightInverse_408 -> ()
d_Carrier_1564 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Level_18
d_Carrier_1564 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₂.isEquivalence
d_isEquivalence_1566 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1566 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsEquivalence_26
d_isEquivalence_1566 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_1566 T_IsRightInverse_408
v8
du_isEquivalence_1566 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1566 :: T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_1566 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Bundles._._.IsRightInverse.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1568 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1568 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1568 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1568 T_IsRightInverse_408
v8
du_isPartialEquivalence_1568 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1568 :: T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1568 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))))
-- Function.Bundles._._.IsRightInverse.Eq₂.partialSetoid
d_partialSetoid_1570 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1570 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_PartialSetoid_10
d_partialSetoid_1570 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_1570 T_IsRightInverse_408
v8
du_partialSetoid_1570 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1570 :: T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_1570 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
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
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsRightInverse.Eq₂.refl
d_refl_1572 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny
d_refl_1572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
d_refl_1572 ~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_IsRightInverse_408
v8 = T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_1572 T_IsRightInverse_408
v8
du_refl_1572 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny
du_refl_1572 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_1572 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsRightInverse.Eq₂.reflexive
d_reflexive_1574 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1574 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1574 T_IsRightInverse_408
v8
du_reflexive_1574 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1574 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1574 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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))
-- Function.Bundles._._.IsRightInverse.Eq₂.setoid
d_setoid_1576 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1576 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Setoid_44
d_setoid_1576 ~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_IsRightInverse_408
v8
  = T_IsRightInverse_408 -> T_Setoid_44
du_setoid_1576 T_IsRightInverse_408
v8
du_setoid_1576 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1576 :: T_IsRightInverse_408 -> T_Setoid_44
du_setoid_1576 T_IsRightInverse_408
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
      ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0))
-- Function.Bundles._._.IsRightInverse.Eq₂.sym
d_sym_1578 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1578 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1578 ~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_IsRightInverse_408
v8 = T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1578 T_IsRightInverse_408
v8
du_sym_1578 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1578 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1578 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsRightInverse.Eq₂.trans
d_trans_1580 ::
  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.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1580 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1580 ~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_IsRightInverse_408
v8 = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1580 T_IsRightInverse_408
v8
du_trans_1580 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1580 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1580 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) 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))))
-- Function.Bundles._._.IsSplitSurjection.from
d_from_1584 ::
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_752 ->
  AgdaAny -> AgdaAny
d_from_1584 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_from_1584 T_IsSplitSurjection_752
v0
  = (T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from_760 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0)
-- Function.Bundles._._.IsSplitSurjection.isLeftInverse
d_isLeftInverse_1596 ::
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_752 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
d_isLeftInverse_1596 :: T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_1596 T_IsSplitSurjection_752
v0
  = (T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0)
-- Function.Bundles._.Equivalence
d_Equivalence_1714 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Equivalence_1714 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Equivalence_1714
  = C_Equivalence'46'constructor_25797 (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Equivalence.to
d_to_1724 :: T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_to_1724 :: T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_to_1724 T_Equivalence_1714
v0
  = case T_Equivalence_1714 -> T_Equivalence_1714
forall a b. a -> b
coe T_Equivalence_1714
v0 of
      C_Equivalence'46'constructor_25797 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Equivalence_1714
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.from
d_from_1726 :: T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_from_1726 :: T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_from_1726 T_Equivalence_1714
v0
  = case T_Equivalence_1714 -> T_Equivalence_1714
forall a b. a -> b
coe T_Equivalence_1714
v0 of
      C_Equivalence'46'constructor_25797 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_Equivalence_1714
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.to-cong
d_to'45'cong_1728 ::
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1728 :: T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1728 T_Equivalence_1714
v0
  = case T_Equivalence_1714 -> T_Equivalence_1714
forall a b. a -> b
coe T_Equivalence_1714
v0 of
      C_Equivalence'46'constructor_25797 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Equivalence_1714
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.from-cong
d_from'45'cong_1730 ::
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1730 :: T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1730 T_Equivalence_1714
v0
  = case T_Equivalence_1714 -> T_Equivalence_1714
forall a b. a -> b
coe T_Equivalence_1714
v0 of
      C_Equivalence'46'constructor_25797 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Equivalence_1714
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.toFunction
d_toFunction_1732 ::
  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 ->
  T_Equivalence_1714 -> T_Func_714
d_toFunction_1732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Func_714
d_toFunction_1732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 T_Equivalence_1714
v6
du_toFunction_1732 :: T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 :: T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 T_Equivalence_1714
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714)
-> AgdaAny -> AgdaAny -> T_Func_714
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714
C_Func'46'constructor_6307 ((T_Equivalence_1714 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_to_1724 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v0))
      ((T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1728 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v0))
-- Function.Bundles._.Equivalence._.isCongruent
d_isCongruent_1736 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1736 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_IsCongruent_22
d_isCongruent_1736 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsCongruent_22
du_isCongruent_1736 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_isCongruent_1736 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1736 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsCongruent_22
du_isCongruent_1736 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2))
-- Function.Bundles._.Equivalence._.Eq₁._≈_
d__'8776'__1740 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1740 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1740 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₁._≉_
d__'8777'__1742 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1742 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1742 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₁.Carrier
d_Carrier_1744 ::
  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 ->
  T_Equivalence_1714 -> ()
d_Carrier_1744 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Level_18
d_Carrier_1744 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₁.isEquivalence
d_isEquivalence_1746 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1746 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_IsEquivalence_26
d_isEquivalence_1746 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsEquivalence_26
du_isEquivalence_1746 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_isEquivalence_1746 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1746 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsEquivalence_26
du_isEquivalence_1746 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Equivalence._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1748 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1748 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1748 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1748 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_isPartialEquivalence_1748 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1748 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1748 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5)))))
-- Function.Bundles._.Equivalence._.Eq₁.partialSetoid
d_partialSetoid_1750 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1750 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_PartialSetoid_10
d_partialSetoid_1750 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_PartialSetoid_10
du_partialSetoid_1750 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_partialSetoid_1750 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1750 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_PartialSetoid_10
du_partialSetoid_1750 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Equivalence._.Eq₁.refl
d_refl_1752 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_refl_1752 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
d_refl_1752 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> AgdaAny -> AgdaAny
du_refl_1752 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_refl_1752 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny
du_refl_1752 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> AgdaAny -> AgdaAny
du_refl_1752 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Equivalence._.Eq₁.reflexive
d_reflexive_1754 ::
  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 ->
  T_Equivalence_1714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1754 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1754 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_reflexive_1754 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1754 :: T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1754 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Equivalence._.Eq₁.setoid
d_setoid_1756 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Setoid_44
d_setoid_1756 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Equivalence_1714 -> T_Setoid_44
du_setoid_1756 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_setoid_1756 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1756 :: T_Setoid_44 -> T_Setoid_44 -> T_Equivalence_1714 -> T_Setoid_44
du_setoid_1756 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Equivalence._.Eq₁.sym
d_sym_1758 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1758 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_sym_1758 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1758 :: T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1758 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Equivalence._.Eq₁.trans
d_trans_1760 ::
  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 ->
  T_Equivalence_1714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1760 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1760 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1760 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_trans_1760 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1760 :: T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1760 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Equivalence._.Eq₂._≈_
d__'8776'__1764 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1764 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₂._≉_
d__'8777'__1766 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1766 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₂.Carrier
d_Carrier_1768 ::
  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 ->
  T_Equivalence_1714 -> ()
d_Carrier_1768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Level_18
d_Carrier_1768 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₂.isEquivalence
d_isEquivalence_1770 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1770 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_IsEquivalence_26
d_isEquivalence_1770 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsEquivalence_26
du_isEquivalence_1770 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_isEquivalence_1770 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1770 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsEquivalence_26
du_isEquivalence_1770 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Equivalence._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1772 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1772 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_isPartialEquivalence_1772 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1772 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1772 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5)))))
-- Function.Bundles._.Equivalence._.Eq₂.partialSetoid
d_partialSetoid_1774 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_PartialSetoid_10
d_partialSetoid_1774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_PartialSetoid_10
du_partialSetoid_1774 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_partialSetoid_1774 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1774 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_PartialSetoid_10
du_partialSetoid_1774 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Equivalence._.Eq₂.refl
d_refl_1776 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_refl_1776 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
d_refl_1776 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> AgdaAny -> AgdaAny
du_refl_1776 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_refl_1776 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny
du_refl_1776 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> AgdaAny -> AgdaAny
du_refl_1776 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Equivalence._.Eq₂.reflexive
d_reflexive_1778 ::
  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 ->
  T_Equivalence_1714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1778 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1778 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1778 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_reflexive_1778 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1778 :: T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1778 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Equivalence._.Eq₂.setoid
d_setoid_1780 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1780 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Setoid_44
d_setoid_1780 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Equivalence_1714 -> T_Setoid_44
du_setoid_1780 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_setoid_1780 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1780 :: T_Setoid_44 -> T_Setoid_44 -> T_Equivalence_1714 -> T_Setoid_44
du_setoid_1780 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Equivalence._.Eq₂.sym
d_sym_1782 ::
  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 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1782 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1782 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_sym_1782 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1782 :: T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1782 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Equivalence._.Eq₂.trans
d_trans_1784 ::
  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 ->
  T_Equivalence_1714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1784 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_trans_1784 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1784 :: T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1784 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = let v3 :: t
v3 = (T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> t
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_toFunction_1732 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) 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
v5)))))
-- Function.Bundles._.Equivalence.fromFunction
d_fromFunction_1786 ::
  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 ->
  T_Equivalence_1714 -> T_Func_714
d_fromFunction_1786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_Func_714
d_fromFunction_1786 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Equivalence_1714 -> T_Func_714
du_fromFunction_1786 T_Equivalence_1714
v6
du_fromFunction_1786 :: T_Equivalence_1714 -> T_Func_714
du_fromFunction_1786 :: T_Equivalence_1714 -> T_Func_714
du_fromFunction_1786 T_Equivalence_1714
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714)
-> AgdaAny -> AgdaAny -> T_Func_714
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714
C_Func'46'constructor_6307 ((T_Equivalence_1714 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714 -> AgdaAny -> AgdaAny
d_from_1726 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v0))
      ((T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1730 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v0))
-- Function.Bundles._.Equivalence._.isCongruent
d_isCongruent_1790 ::
  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 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Equivalence_1714
-> T_IsCongruent_22
d_isCongruent_1790 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsCongruent_22
du_isCongruent_1790 T_Setoid_44
v4 T_Setoid_44
v5 T_Equivalence_1714
v6
du_isCongruent_1790 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Equivalence_1714 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1790 :: T_Setoid_44
-> T_Setoid_44 -> T_Equivalence_1714 -> T_IsCongruent_22
du_isCongruent_1790 T_Setoid_44
v0 T_Setoid_44
v1 T_Equivalence_1714
v2
  = (T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_44 -> T_Setoid_44 -> T_Func_714 -> T_IsCongruent_22
du_isCongruent_724 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0)
      ((T_Equivalence_1714 -> T_Func_714) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714 -> T_Func_714
du_fromFunction_1786 (T_Equivalence_1714 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1714
v2))
-- Function.Bundles._.LeftInverse
d_LeftInverse_1792 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_LeftInverse_1792 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_LeftInverse_1792
  = C_LeftInverse'46'constructor_29775 (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.LeftInverse.to
d_to_1804 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_to_1804 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_to_1804 T_LeftInverse_1792
v0
  = case T_LeftInverse_1792 -> T_LeftInverse_1792
forall a b. a -> b
coe T_LeftInverse_1792
v0 of
      C_LeftInverse'46'constructor_29775 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_LeftInverse_1792
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.from
d_from_1806 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 T_LeftInverse_1792
v0
  = case T_LeftInverse_1792 -> T_LeftInverse_1792
forall a b. a -> b
coe T_LeftInverse_1792
v0 of
      C_LeftInverse'46'constructor_29775 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_LeftInverse_1792
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.to-cong
d_to'45'cong_1808 ::
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1808 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1808 T_LeftInverse_1792
v0
  = case T_LeftInverse_1792 -> T_LeftInverse_1792
forall a b. a -> b
coe T_LeftInverse_1792
v0 of
      C_LeftInverse'46'constructor_29775 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_LeftInverse_1792
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.from-cong
d_from'45'cong_1810 ::
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1810 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1810 T_LeftInverse_1792
v0
  = case T_LeftInverse_1792 -> T_LeftInverse_1792
forall a b. a -> b
coe T_LeftInverse_1792
v0 of
      C_LeftInverse'46'constructor_29775 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_LeftInverse_1792
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.inverseˡ
d_inverse'737'_1812 ::
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1812 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1812 T_LeftInverse_1792
v0
  = case T_LeftInverse_1792 -> T_LeftInverse_1792
forall a b. a -> b
coe T_LeftInverse_1792
v0 of
      C_LeftInverse'46'constructor_29775 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_LeftInverse_1792
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.isCongruent
d_isCongruent_1814 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1814 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsCongruent_22
d_isCongruent_1814 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22
du_isCongruent_1814 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isCongruent_1814 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1814 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22
du_isCongruent_1814 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1808 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((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_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))
-- Function.Bundles._.LeftInverse.isLeftInverse
d_isLeftInverse_1816 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
d_isLeftInverse_1816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsLeftInverse_322
d_isLeftInverse_1816 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isLeftInverse_1816 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
du_isLeftInverse_1816 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.C_IsLeftInverse'46'constructor_14363
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22
du_isCongruent_1814 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1810 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1812 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
-- Function.Bundles._.LeftInverse._.isSurjection
d_isSurjection_1820 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
d_isSurjection_1820 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsSurjection_162
d_isSurjection_1820 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSurjection_162
du_isSurjection_1820 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isSurjection_1820 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
du_isSurjection_1820 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSurjection_162
du_isSurjection_1820 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
MAlonzo.Code.Function.Structures.du_isSurjection_400
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
-- Function.Bundles._.LeftInverse._.strictlyInverseˡ
d_strictlyInverse'737'_1822 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_1822 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_1822 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1822 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_strictlyInverse'737'_1822 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1822 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1822 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_396
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
-- Function.Bundles._.LeftInverse._.Eq₁._≈_
d__'8776'__1826 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1826 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁._≉_
d__'8777'__1828 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1828 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1828 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁.Carrier
d_Carrier_1830 ::
  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 ->
  T_LeftInverse_1792 -> ()
d_Carrier_1830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
d_Carrier_1830 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁.isEquivalence
d_isEquivalence_1832 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsEquivalence_26
d_isEquivalence_1832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_1832 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isEquivalence_1832 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1832 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_1832 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4)))
-- Function.Bundles._.LeftInverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1834 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1834 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isPartialEquivalence_1834 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1834 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1834 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₁.partialSetoid
d_partialSetoid_1836 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_PartialSetoid_10
d_partialSetoid_1836 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_1836 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_partialSetoid_1836 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1836 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_1836 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.LeftInverse._.Eq₁.refl
d_refl_1838 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_refl_1838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
d_refl_1838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_1838 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_refl_1838 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_1838 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_1838 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.LeftInverse._.Eq₁.reflexive
d_reflexive_1840 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1840 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_reflexive_1840 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1840 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1840 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.LeftInverse._.Eq₁.setoid
d_setoid_1842 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Setoid_44
d_setoid_1842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_1842 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_setoid_1842 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1842 :: T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_1842 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₁.sym
d_sym_1844 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1844 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_sym_1844 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1844 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1844 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₁.trans
d_trans_1846 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1846 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1846 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_trans_1846 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1846 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1846 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₂._≈_
d__'8776'__1850 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1850 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂._≉_
d__'8777'__1852 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1852 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1852 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂.Carrier
d_Carrier_1854 ::
  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 ->
  T_LeftInverse_1792 -> ()
d_Carrier_1854 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
d_Carrier_1854 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂.isEquivalence
d_isEquivalence_1856 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1856 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsEquivalence_26
d_isEquivalence_1856 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_1856 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isEquivalence_1856 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1856 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_1856 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4)))
-- Function.Bundles._.LeftInverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1858 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1858 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1858 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isPartialEquivalence_1858 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1858 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1858 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₂.partialSetoid
d_partialSetoid_1860 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1860 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_PartialSetoid_10
d_partialSetoid_1860 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_1860 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_partialSetoid_1860 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1860 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_1860 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.LeftInverse._.Eq₂.refl
d_refl_1862 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_refl_1862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
d_refl_1862 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_1862 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_refl_1862 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_1862 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_1862 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.LeftInverse._.Eq₂.reflexive
d_reflexive_1864 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1864 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1864 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_reflexive_1864 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1864 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1864 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.LeftInverse._.Eq₂.setoid
d_setoid_1866 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Setoid_44
d_setoid_1866 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_1866 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_setoid_1866 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1866 :: T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_1866 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₂.sym
d_sym_1868 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1868 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1868 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1868 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_sym_1868 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1868 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1868 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₂.trans
d_trans_1870 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1870 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1870 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1870 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_trans_1870 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1870 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1870 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.LeftInverse.equivalence
d_equivalence_1872 ::
  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 ->
  T_LeftInverse_1792 -> T_Equivalence_1714
d_equivalence_1872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Equivalence_1714
d_equivalence_1872 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_LeftInverse_1792 -> T_Equivalence_1714
du_equivalence_1872 T_LeftInverse_1792
v6
du_equivalence_1872 :: T_LeftInverse_1792 -> T_Equivalence_1714
du_equivalence_1872 :: T_LeftInverse_1792 -> T_Equivalence_1714
du_equivalence_1872 T_LeftInverse_1792
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_1714)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_1714
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_1714
C_Equivalence'46'constructor_25797 ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_to_1804 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0))
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)) ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1808 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0))
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1810 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0))
-- Function.Bundles._.LeftInverse.isSplitSurjection
d_isSplitSurjection_1874 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_752
d_isSplitSurjection_1874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsSplitSurjection_752
d_isSplitSurjection_1874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSplitSurjection_752
du_isSplitSurjection_1874 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isSplitSurjection_1874 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_752
du_isSplitSurjection_1874 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSplitSurjection_752
du_isSplitSurjection_1874 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = ((AgdaAny -> AgdaAny)
 -> T_IsLeftInverse_322 -> T_IsSplitSurjection_752)
-> AgdaAny -> AgdaAny -> T_IsSplitSurjection_752
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322 -> T_IsSplitSurjection_752
MAlonzo.Code.Function.Structures.C_IsSplitSurjection'46'constructor_35501
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
-- Function.Bundles._.LeftInverse.surjection
d_surjection_1876 ::
  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 ->
  T_LeftInverse_1792 -> T_Surjection_846
d_surjection_1876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Surjection_846
d_surjection_1876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_LeftInverse_1792 -> T_Surjection_846
du_surjection_1876 T_LeftInverse_1792
v6
du_surjection_1876 :: T_LeftInverse_1792 -> T_Surjection_846
du_surjection_1876 :: T_LeftInverse_1792 -> T_Surjection_846
du_surjection_1876 T_LeftInverse_1792
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_846)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_846
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_846
C_Surjection'46'constructor_11197 ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_to_1804 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0))
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1808 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0))
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 ->
            (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 T_LeftInverse_1792
v0 AgdaAny
v1)
              ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1812 T_LeftInverse_1792
v0 AgdaAny
v1)))
-- Function.Bundles._.RightInverse
d_RightInverse_1880 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_RightInverse_1880 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_RightInverse_1880
  = C_RightInverse'46'constructor_34573 (AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.RightInverse.to
d_to_1892 :: T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_to_1892 :: T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_to_1892 T_RightInverse_1880
v0
  = case T_RightInverse_1880 -> T_RightInverse_1880
forall a b. a -> b
coe T_RightInverse_1880
v0 of
      C_RightInverse'46'constructor_34573 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_RightInverse_1880
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.from
d_from_1894 :: T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_from_1894 :: T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_from_1894 T_RightInverse_1880
v0
  = case T_RightInverse_1880 -> T_RightInverse_1880
forall a b. a -> b
coe T_RightInverse_1880
v0 of
      C_RightInverse'46'constructor_34573 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_RightInverse_1880
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.to-cong
d_to'45'cong_1896 ::
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1896 :: T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1896 T_RightInverse_1880
v0
  = case T_RightInverse_1880 -> T_RightInverse_1880
forall a b. a -> b
coe T_RightInverse_1880
v0 of
      C_RightInverse'46'constructor_34573 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RightInverse_1880
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.from-cong
d_from'45'cong_1898 ::
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1898 :: T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1898 T_RightInverse_1880
v0
  = case T_RightInverse_1880 -> T_RightInverse_1880
forall a b. a -> b
coe T_RightInverse_1880
v0 of
      C_RightInverse'46'constructor_34573 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RightInverse_1880
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.inverseʳ
d_inverse'691'_1900 ::
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1900 :: T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1900 T_RightInverse_1880
v0
  = case T_RightInverse_1880 -> T_RightInverse_1880
forall a b. a -> b
coe T_RightInverse_1880
v0 of
      C_RightInverse'46'constructor_34573 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_RightInverse_1880
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.isCongruent
d_isCongruent_1902 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_IsCongruent_22
d_isCongruent_1902 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsCongruent_22
du_isCongruent_1902 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_isCongruent_1902 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1902 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsCongruent_22
du_isCongruent_1902 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1896 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2))
      ((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_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))
-- Function.Bundles._.RightInverse.isRightInverse
d_isRightInverse_1904 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408
d_isRightInverse_1904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_IsRightInverse_408
d_isRightInverse_1904 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_isRightInverse_1904 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408
du_isRightInverse_1904 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
MAlonzo.Code.Function.Structures.C_IsRightInverse'46'constructor_18837
      ((T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsCongruent_22
du_isCongruent_1902 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2))
      ((T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1898 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2))
      ((T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1900 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2))
-- Function.Bundles._.RightInverse._.strictlyInverseʳ
d_strictlyInverse'691'_1908 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_1908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_1908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_1908 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_strictlyInverse'691'_1908 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_1908 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_1908 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = ((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'691'_482
      ((T_RightInverse_1880 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_to_1892 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2))
      ((T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2))
-- Function.Bundles._.RightInverse._.Eq₁._≈_
d__'8776'__1912 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1912 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₁._≉_
d__'8777'__1914 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1914 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₁.Carrier
d_Carrier_1916 ::
  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 ->
  T_RightInverse_1880 -> ()
d_Carrier_1916 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_Level_18
d_Carrier_1916 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₁.isEquivalence
d_isEquivalence_1918 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_IsEquivalence_26
d_isEquivalence_1918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsEquivalence_26
du_isEquivalence_1918 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_isEquivalence_1918 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1918 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsEquivalence_26
du_isEquivalence_1918 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4)))
-- Function.Bundles._.RightInverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1920 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1920 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_isPartialEquivalence_1920 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1920 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1920 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5)))))
-- Function.Bundles._.RightInverse._.Eq₁.partialSetoid
d_partialSetoid_1922 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_PartialSetoid_10
d_partialSetoid_1922 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_PartialSetoid_10
du_partialSetoid_1922 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_partialSetoid_1922 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1922 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_PartialSetoid_10
du_partialSetoid_1922 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.RightInverse._.Eq₁.refl
d_refl_1924 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_refl_1924 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
d_refl_1924 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_refl_1924 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_refl_1924 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_refl_1924 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_refl_1924 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.RightInverse._.Eq₁.reflexive
d_reflexive_1926 ::
  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 ->
  T_RightInverse_1880 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1926 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1926 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1926 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_reflexive_1926 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1926 :: T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1926 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.RightInverse._.Eq₁.setoid
d_setoid_1928 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1928 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_Setoid_44
d_setoid_1928 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44 -> T_Setoid_44 -> T_RightInverse_1880 -> T_Setoid_44
du_setoid_1928 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_setoid_1928 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1928 :: T_Setoid_44 -> T_Setoid_44 -> T_RightInverse_1880 -> T_Setoid_44
du_setoid_1928 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.RightInverse._.Eq₁.sym
d_sym_1930 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1930 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1930 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1930 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_sym_1930 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1930 :: T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1930 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.RightInverse._.Eq₁.trans
d_trans_1932 ::
  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 ->
  T_RightInverse_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1932 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1932 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1932 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_trans_1932 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1932 :: T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1932 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.RightInverse._.Eq₂._≈_
d__'8776'__1936 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1936 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1936 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₂._≉_
d__'8777'__1938 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1938 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1938 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₂.Carrier
d_Carrier_1940 ::
  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 ->
  T_RightInverse_1880 -> ()
d_Carrier_1940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_Level_18
d_Carrier_1940 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₂.isEquivalence
d_isEquivalence_1942 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1942 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_IsEquivalence_26
d_isEquivalence_1942 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsEquivalence_26
du_isEquivalence_1942 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_isEquivalence_1942 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1942 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsEquivalence_26
du_isEquivalence_1942 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4)))
-- Function.Bundles._.RightInverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1944 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1944 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1944 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1944 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_isPartialEquivalence_1944 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1944 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1944 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5)))))
-- Function.Bundles._.RightInverse._.Eq₂.partialSetoid
d_partialSetoid_1946 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_PartialSetoid_10
d_partialSetoid_1946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_PartialSetoid_10
du_partialSetoid_1946 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_partialSetoid_1946 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1946 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_PartialSetoid_10
du_partialSetoid_1946 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.RightInverse._.Eq₂.refl
d_refl_1948 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_refl_1948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
d_refl_1948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_refl_1948 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_refl_1948 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_refl_1948 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> AgdaAny -> AgdaAny
du_refl_1948 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.RightInverse._.Eq₂.reflexive
d_reflexive_1950 ::
  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 ->
  T_RightInverse_1880 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1950 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1950 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1950 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_reflexive_1950 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1950 :: T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1950 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.RightInverse._.Eq₂.setoid
d_setoid_1952 ::
  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 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1952 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_Setoid_44
d_setoid_1952 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44 -> T_Setoid_44 -> T_RightInverse_1880 -> T_Setoid_44
du_setoid_1952 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_setoid_1952 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1952 :: T_Setoid_44 -> T_Setoid_44 -> T_RightInverse_1880 -> T_Setoid_44
du_setoid_1952 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.RightInverse._.Eq₂.sym
d_sym_1954 ::
  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 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1954 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_sym_1954 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1954 :: T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1954 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.RightInverse._.Eq₂.trans
d_trans_1956 ::
  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 ->
  T_RightInverse_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1956 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1956 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6 = T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1956 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1880
v6
du_trans_1956 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1956 :: T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1956 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1880
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_408 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_420 (AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.RightInverse.equivalence
d_equivalence_1958 ::
  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 ->
  T_RightInverse_1880 -> T_Equivalence_1714
d_equivalence_1958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1880
-> T_Equivalence_1714
d_equivalence_1958 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_RightInverse_1880
v6
  = T_RightInverse_1880 -> T_Equivalence_1714
du_equivalence_1958 T_RightInverse_1880
v6
du_equivalence_1958 :: T_RightInverse_1880 -> T_Equivalence_1714
du_equivalence_1958 :: T_RightInverse_1880 -> T_Equivalence_1714
du_equivalence_1958 T_RightInverse_1880
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_1714)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_1714
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_1714
C_Equivalence'46'constructor_25797 ((T_RightInverse_1880 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_to_1892 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v0))
      ((T_RightInverse_1880 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_from_1894 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v0)) ((T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1896 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v0))
      ((T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1898 (T_RightInverse_1880 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880
v0))
-- Function.Bundles._.Inverse
d_Inverse_1960 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Inverse_1960 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Inverse_1960
  = C_Inverse'46'constructor_38621 (AgdaAny -> AgdaAny)
                                   (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Function.Bundles._.Inverse.to
d_to_1972 :: T_Inverse_1960 -> AgdaAny -> AgdaAny
d_to_1972 :: T_Inverse_1960 -> AgdaAny -> AgdaAny
d_to_1972 T_Inverse_1960
v0
  = case T_Inverse_1960 -> T_Inverse_1960
forall a b. a -> b
coe T_Inverse_1960
v0 of
      C_Inverse'46'constructor_38621 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Inverse_1960
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.from
d_from_1974 :: T_Inverse_1960 -> AgdaAny -> AgdaAny
d_from_1974 :: T_Inverse_1960 -> AgdaAny -> AgdaAny
d_from_1974 T_Inverse_1960
v0
  = case T_Inverse_1960 -> T_Inverse_1960
forall a b. a -> b
coe T_Inverse_1960
v0 of
      C_Inverse'46'constructor_38621 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_Inverse_1960
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.to-cong
d_to'45'cong_1976 ::
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1976 :: T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1976 T_Inverse_1960
v0
  = case T_Inverse_1960 -> T_Inverse_1960
forall a b. a -> b
coe T_Inverse_1960
v0 of
      C_Inverse'46'constructor_38621 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
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_Inverse_1960
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.from-cong
d_from'45'cong_1978 ::
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1978 :: T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1978 T_Inverse_1960
v0
  = case T_Inverse_1960 -> T_Inverse_1960
forall a b. a -> b
coe T_Inverse_1960
v0 of
      C_Inverse'46'constructor_38621 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Inverse_1960
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.inverse
d_inverse_1980 ::
  T_Inverse_1960 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1980 :: T_Inverse_1960 -> T_Σ_14
d_inverse_1980 T_Inverse_1960
v0
  = case T_Inverse_1960 -> T_Inverse_1960
forall a b. a -> b
coe T_Inverse_1960
v0 of
      C_Inverse'46'constructor_38621 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v5
      T_Inverse_1960
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.inverseˡ
d_inverse'737'_1982 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_inverse'737'_1982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1960
v6 AgdaAny
v7 AgdaAny
v8
  = T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_1982 T_Inverse_1960
v6 AgdaAny
v7 AgdaAny
v8
du_inverse'737'_1982 ::
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_1982 :: T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_1982 T_Inverse_1960
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny)
-> 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_Inverse_1960 -> T_Σ_14
d_inverse_1980 (T_Inverse_1960 -> T_Inverse_1960
forall a b. a -> b
coe T_Inverse_1960
v0))
      AgdaAny
v1 AgdaAny
v2
-- Function.Bundles._.Inverse.inverseʳ
d_inverse'691'_1984 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_inverse'691'_1984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1960
v6 AgdaAny
v7 AgdaAny
v8
  = T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_1984 T_Inverse_1960
v6 AgdaAny
v7 AgdaAny
v8
du_inverse'691'_1984 ::
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_1984 :: T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_1984 T_Inverse_1960
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny)
-> 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_Inverse_1960 -> T_Σ_14
d_inverse_1980 (T_Inverse_1960 -> T_Inverse_1960
forall a b. a -> b
coe T_Inverse_1960
v0))
      AgdaAny
v1 AgdaAny
v2
-- Function.Bundles._.Inverse.leftInverse
d_leftInverse_1986 ::
  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 ->
  T_Inverse_1960 -> T_LeftInverse_1792
d_leftInverse_1986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_LeftInverse_1792
d_leftInverse_1986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Inverse_1960 -> T_LeftInverse_1792
du_leftInverse_1986 T_Inverse_1960
v6
du_leftInverse_1986 :: T_Inverse_1960 -> T_LeftInverse_1792
du_leftInverse_1986 :: T_Inverse_1960 -> T_LeftInverse_1792
du_leftInverse_1986 T_Inverse_1960
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_LeftInverse_1792)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_LeftInverse_1792
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1792
C_LeftInverse'46'constructor_29775 ((T_Inverse_1960 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny
d_to_1972 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
      ((T_Inverse_1960 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny
d_from_1974 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0)) ((T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1976 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
      ((T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1978 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
      ((T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_1982 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
-- Function.Bundles._.Inverse.rightInverse
d_rightInverse_1988 ::
  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 ->
  T_Inverse_1960 -> T_RightInverse_1880
d_rightInverse_1988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_RightInverse_1880
d_rightInverse_1988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Inverse_1960 -> T_RightInverse_1880
du_rightInverse_1988 T_Inverse_1960
v6
du_rightInverse_1988 :: T_Inverse_1960 -> T_RightInverse_1880
du_rightInverse_1988 :: T_Inverse_1960 -> T_RightInverse_1880
du_rightInverse_1988 T_Inverse_1960
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_RightInverse_1880)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_RightInverse_1880
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_RightInverse_1880
C_RightInverse'46'constructor_34573 ((T_Inverse_1960 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny
d_to_1972 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
      ((T_Inverse_1960 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny
d_from_1974 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0)) ((T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1976 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
      ((T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1978 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
      ((T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_1984 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v0))
-- Function.Bundles._.Inverse._.isLeftInverse
d_isLeftInverse_1992 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
d_isLeftInverse_1992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_IsLeftInverse_322
d_isLeftInverse_1992 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsLeftInverse_322
du_isLeftInverse_1992 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_isLeftInverse_1992 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
du_isLeftInverse_1992 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsLeftInverse_322
du_isLeftInverse_1992 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe
      T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Inverse_1960 -> T_LeftInverse_1792) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> T_LeftInverse_1792
du_leftInverse_1986 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2))
-- Function.Bundles._.Inverse._.strictlyInverseˡ
d_strictlyInverse'737'_1994 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_1994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_1994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1994 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_strictlyInverse'737'_1994 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1994 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1994 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Inverse_1960 -> T_LeftInverse_1792) -> AgdaAny -> t
forall a b. a -> b
coe T_Inverse_1960 -> T_LeftInverse_1792
du_leftInverse_1986 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_396
         ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
         ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Inverse._.isRightInverse
d_isRightInverse_1998 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408
d_isRightInverse_1998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_IsRightInverse_408
d_isRightInverse_1998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1960 -> T_IsRightInverse_408
du_isRightInverse_1998 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_isRightInverse_1998 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_408
du_isRightInverse_1998 :: T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1960 -> T_IsRightInverse_408
du_isRightInverse_1998 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe
      T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Inverse_1960 -> T_RightInverse_1880) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> T_RightInverse_1880
du_rightInverse_1988 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2))
-- Function.Bundles._.Inverse._.strictlyInverseʳ
d_strictlyInverse'691'_2000 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_2000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_2000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2000 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_strictlyInverse'691'_2000 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2000 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2000 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Inverse_1960 -> T_RightInverse_1880) -> AgdaAny -> t
forall a b. a -> b
coe T_Inverse_1960 -> T_RightInverse_1880
du_rightInverse_1988 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'691'_482
         ((T_RightInverse_1880 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1880 -> AgdaAny -> AgdaAny
d_to_1892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
         ((T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1880 -> T_IsRightInverse_408
du_isRightInverse_1904 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Inverse.isInverse
d_isInverse_2002 ::
  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 ->
  T_Inverse_1960 -> MAlonzo.Code.Function.Structures.T_IsInverse_490
d_isInverse_2002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_IsInverse_490
d_isInverse_2002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_isInverse_2002 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> MAlonzo.Code.Function.Structures.T_IsInverse_490
du_isInverse_2002 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = (T_IsLeftInverse_322
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe
      T_IsLeftInverse_322
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInverse_490
MAlonzo.Code.Function.Structures.C_IsInverse'46'constructor_22449
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
         ((T_Inverse_1960 -> T_LeftInverse_1792) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> T_LeftInverse_1792
du_leftInverse_1986 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2)))
      ((T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_1984 (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2))
-- Function.Bundles._.Inverse._.Eq₁._≈_
d__'8776'__2008 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2008 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁._≉_
d__'8777'__2010 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2010 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁.Carrier
d_Carrier_2012 ::
  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 ->
  T_Inverse_1960 -> ()
d_Carrier_2012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_Level_18
d_Carrier_2012 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁.isEquivalence
d_isEquivalence_2014 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_IsEquivalence_26
d_isEquivalence_2014 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsEquivalence_26
du_isEquivalence_2014 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_isEquivalence_2014 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2014 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsEquivalence_26
du_isEquivalence_2014 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Inverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_2016 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2016 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2016 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1960 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2016 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_isPartialEquivalence_2016 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2016 :: T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1960 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2016 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))))))
-- Function.Bundles._.Inverse._.Eq₁.partialSetoid
d_partialSetoid_2018 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2018 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_PartialSetoid_10
d_partialSetoid_2018 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_PartialSetoid_10
du_partialSetoid_2018 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_partialSetoid_2018 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2018 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_PartialSetoid_10
du_partialSetoid_2018 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
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
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₁.refl
d_refl_2020 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
d_refl_2020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
d_refl_2020 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_refl_2020 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_refl_2020 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
du_refl_2020 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_refl_2020 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₁.reflexive
d_reflexive_2022 ::
  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 ->
  T_Inverse_1960 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2022 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2022 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_reflexive_2022 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2022 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2022 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Inverse._.Eq₁.setoid
d_setoid_2024 ::
  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 ->
  T_Inverse_1960 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_Setoid_44
d_setoid_2024 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_Setoid_44
du_setoid_2024 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_setoid_2024 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2024 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_Setoid_44
du_setoid_2024 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
            ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v4))))
-- Function.Bundles._.Inverse._.Eq₁.sym
d_sym_2026 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2026 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2026 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2026 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_sym_2026 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2026 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2026 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._.Inverse._.Eq₁.trans
d_trans_2028 ::
  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 ->
  T_Inverse_1960 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2028 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_trans_2028 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2028 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2028 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._.Inverse._.Eq₂._≈_
d__'8776'__2032 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2032 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂._≉_
d__'8777'__2034 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2034 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2034 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂.Carrier
d_Carrier_2036 ::
  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 ->
  T_Inverse_1960 -> ()
d_Carrier_2036 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_Level_18
d_Carrier_2036 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂.isEquivalence
d_isEquivalence_2038 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2038 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_IsEquivalence_26
d_isEquivalence_2038 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsEquivalence_26
du_isEquivalence_2038 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_isEquivalence_2038 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2038 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsEquivalence_26
du_isEquivalence_2038 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Inverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_2040 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2040 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2040 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1960 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2040 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_isPartialEquivalence_2040 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2040 :: T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1960 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2040 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))))))
-- Function.Bundles._.Inverse._.Eq₂.partialSetoid
d_partialSetoid_2042 ::
  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 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2042 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_PartialSetoid_10
d_partialSetoid_2042 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_PartialSetoid_10
du_partialSetoid_2042 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_partialSetoid_2042 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2042 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_PartialSetoid_10
du_partialSetoid_2042 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
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
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₂.refl
d_refl_2044 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
d_refl_2044 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
d_refl_2044 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_refl_2044 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_refl_2044 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny
du_refl_2044 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> AgdaAny -> AgdaAny
du_refl_2044 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₂.reflexive
d_reflexive_2046 ::
  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 ->
  T_Inverse_1960 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2046 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2046 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2046 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_reflexive_2046 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2046 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2046 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Inverse._.Eq₂.setoid
d_setoid_2048 ::
  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 ->
  T_Inverse_1960 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2048 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> T_Setoid_44
d_setoid_2048 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_Setoid_44
du_setoid_2048 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_setoid_2048 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2048 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_Setoid_44
du_setoid_2048 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
            ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v4))))
-- Function.Bundles._.Inverse._.Eq₂.sym
d_sym_2050 ::
  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 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2050 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2050 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2050 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_sym_2050 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2050 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2050 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._.Inverse._.Eq₂.trans
d_trans_2052 ::
  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 ->
  T_Inverse_1960 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2052 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2052 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2052 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1960
v6
du_trans_2052 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1960 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2052 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1960
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2052 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1960
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1960 -> T_IsInverse_490
du_isInverse_2002 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1960 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1960
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_322
v4
             = T_IsInverse_490 -> T_IsLeftInverse_322
MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (AgdaAny -> T_IsInverse_490
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) 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
v6))))))
-- Function.Bundles._.BiEquivalence
d_BiEquivalence_2054 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_BiEquivalence_2054 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_BiEquivalence_2054
  = C_BiEquivalence'46'constructor_44693 (AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.BiEquivalence.to
d_to_2068 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny
d_to_2068 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny
d_to_2068 T_BiEquivalence_2054
v0
  = case T_BiEquivalence_2054 -> T_BiEquivalence_2054
forall a b. a -> b
coe T_BiEquivalence_2054
v0 of
      C_BiEquivalence'46'constructor_44693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_BiEquivalence_2054
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₁
d_from'8321'_2070 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny
d_from'8321'_2070 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny
d_from'8321'_2070 T_BiEquivalence_2054
v0
  = case T_BiEquivalence_2054 -> T_BiEquivalence_2054
forall a b. a -> b
coe T_BiEquivalence_2054
v0 of
      C_BiEquivalence'46'constructor_44693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_BiEquivalence_2054
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₂
d_from'8322'_2072 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny
d_from'8322'_2072 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny
d_from'8322'_2072 T_BiEquivalence_2054
v0
  = case T_BiEquivalence_2054 -> T_BiEquivalence_2054
forall a b. a -> b
coe T_BiEquivalence_2054
v0 of
      C_BiEquivalence'46'constructor_44693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_BiEquivalence_2054
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.to-cong
d_to'45'cong_2074 ::
  T_BiEquivalence_2054 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2074 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2074 T_BiEquivalence_2054
v0
  = case T_BiEquivalence_2054 -> T_BiEquivalence_2054
forall a b. a -> b
coe T_BiEquivalence_2054
v0 of
      C_BiEquivalence'46'constructor_44693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BiEquivalence_2054
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₁-cong
d_from'8321''45'cong_2076 ::
  T_BiEquivalence_2054 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2076 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2076 T_BiEquivalence_2054
v0
  = case T_BiEquivalence_2054 -> T_BiEquivalence_2054
forall a b. a -> b
coe T_BiEquivalence_2054
v0 of
      C_BiEquivalence'46'constructor_44693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_BiEquivalence_2054
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₂-cong
d_from'8322''45'cong_2078 ::
  T_BiEquivalence_2054 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2078 :: T_BiEquivalence_2054 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2078 T_BiEquivalence_2054
v0
  = case T_BiEquivalence_2054 -> T_BiEquivalence_2054
forall a b. a -> b
coe T_BiEquivalence_2054
v0 of
      C_BiEquivalence'46'constructor_44693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
      T_BiEquivalence_2054
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse
d_BiInverse_2080 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_BiInverse_2080 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_BiInverse_2080
  = C_BiInverse'46'constructor_47439 (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)
-- Function.Bundles._.BiInverse.to
d_to_2098 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_to_2098 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_to_2098 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₁
d_from'8321'_2100 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_from'8321'_2100 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_from'8321'_2100 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₂
d_from'8322'_2102 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_from'8322'_2102 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_from'8322'_2102 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.to-cong
d_to'45'cong_2104 ::
  T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2104 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2104 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₁-cong
d_from'8321''45'cong_2106 ::
  T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2106 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2106 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₂-cong
d_from'8322''45'cong_2108 ::
  T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2108 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2108 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.inverseˡ
d_inverse'737'_2110 ::
  T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2110 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2110 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.inverseʳ
d_inverse'691'_2112 ::
  T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2112 :: T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2112 T_BiInverse_2080
v0
  = case T_BiInverse_2080 -> T_BiInverse_2080
forall a b. a -> b
coe T_BiInverse_2080
v0 of
      C_BiInverse'46'constructor_47439 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v8
      T_BiInverse_2080
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.to-isCongruent
d_to'45'isCongruent_2114 ::
  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 ->
  T_BiInverse_2080 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_to'45'isCongruent_2114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_BiInverse_2080
-> T_IsCongruent_22
d_to'45'isCongruent_2114 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_2080
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_2080 -> T_IsCongruent_22
du_to'45'isCongruent_2114 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_2080
v6
du_to'45'isCongruent_2114 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_BiInverse_2080 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_to'45'isCongruent_2114 :: T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_2080 -> T_IsCongruent_22
du_to'45'isCongruent_2114 T_Setoid_44
v0 T_Setoid_44
v1 T_BiInverse_2080
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2104 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v2))
      ((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_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))
-- Function.Bundles._.BiInverse.isBiInverse
d_isBiInverse_2116 ::
  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 ->
  T_BiInverse_2080 ->
  MAlonzo.Code.Function.Structures.T_IsBiInverse_666
d_isBiInverse_2116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_BiInverse_2080
-> T_IsBiInverse_666
d_isBiInverse_2116 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_2080
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_2080 -> T_IsBiInverse_666
du_isBiInverse_2116 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_2080
v6
du_isBiInverse_2116 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_BiInverse_2080 ->
  MAlonzo.Code.Function.Structures.T_IsBiInverse_666
du_isBiInverse_2116 :: T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_2080 -> T_IsBiInverse_666
du_isBiInverse_2116 T_Setoid_44
v0 T_Setoid_44
v1 T_BiInverse_2080
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsBiInverse_666)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsBiInverse_666
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
MAlonzo.Code.Function.Structures.C_IsBiInverse'46'constructor_32731
      ((T_Setoid_44
 -> T_Setoid_44 -> T_BiInverse_2080 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_2080 -> T_IsCongruent_22
du_to'45'isCongruent_2114 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v2))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2106 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v2))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2108 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v2))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2110 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v2))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2112 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v2))
-- Function.Bundles._.BiInverse.biEquivalence
d_biEquivalence_2118 ::
  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 ->
  T_BiInverse_2080 -> T_BiEquivalence_2054
d_biEquivalence_2118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_BiInverse_2080
-> T_BiEquivalence_2054
d_biEquivalence_2118 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_BiInverse_2080
v6
  = T_BiInverse_2080 -> T_BiEquivalence_2054
du_biEquivalence_2118 T_BiInverse_2080
v6
du_biEquivalence_2118 :: T_BiInverse_2080 -> T_BiEquivalence_2054
du_biEquivalence_2118 :: T_BiInverse_2080 -> T_BiEquivalence_2054
du_biEquivalence_2118 T_BiInverse_2080
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_BiEquivalence_2054)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_BiEquivalence_2054
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BiEquivalence_2054
C_BiEquivalence'46'constructor_44693 ((T_BiInverse_2080 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_to_2098 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v0))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_from'8321'_2100 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v0)) ((T_BiInverse_2080 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny
d_from'8322'_2102 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v0))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2104 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v0))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2106 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v0))
      ((T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2108 (T_BiInverse_2080 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2080
v0))
-- Function.Bundles._.SplitSurjection
d_SplitSurjection_2120 ::
  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_SplitSurjection_2120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
d_SplitSurjection_2120 = 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.Bundles._.SplitSurjection.equivalence
d_equivalence_2126 ::
  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 ->
  T_LeftInverse_1792 -> T_Equivalence_1714
d_equivalence_2126 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Equivalence_1714
d_equivalence_2126 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_LeftInverse_1792 -> T_Equivalence_1714
du_equivalence_2126 T_LeftInverse_1792
v6
du_equivalence_2126 :: T_LeftInverse_1792 -> T_Equivalence_1714
du_equivalence_2126 :: T_LeftInverse_1792 -> T_Equivalence_1714
du_equivalence_2126 T_LeftInverse_1792
v0 = (T_LeftInverse_1792 -> T_Equivalence_1714)
-> AgdaAny -> T_Equivalence_1714
forall a b. a -> b
coe T_LeftInverse_1792 -> T_Equivalence_1714
du_equivalence_1872 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)
-- Function.Bundles._.SplitSurjection.from
d_from_2128 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_2128 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_2128 T_LeftInverse_1792
v0 = (T_LeftInverse_1792 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)
-- Function.Bundles._.SplitSurjection.from-cong
d_from'45'cong_2130 ::
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2130 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2130 T_LeftInverse_1792
v0 = (T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1810 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)
-- Function.Bundles._.SplitSurjection.inverseˡ
d_inverse'737'_2132 ::
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2132 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2132 T_LeftInverse_1792
v0 = (T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1812 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)
-- Function.Bundles._.SplitSurjection.isCongruent
d_isCongruent_2134 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_2134 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsCongruent_22
d_isCongruent_2134 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22
du_isCongruent_2134 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isCongruent_2134 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_2134 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22
du_isCongruent_2134 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsCongruent_22
du_isCongruent_1814 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2)
-- Function.Bundles._.SplitSurjection.isLeftInverse
d_isLeftInverse_2136 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
d_isLeftInverse_2136 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsLeftInverse_322
d_isLeftInverse_2136 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_2136 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isLeftInverse_2136 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
du_isLeftInverse_2136 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_2136 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2)
-- Function.Bundles._.SplitSurjection.isSplitSurjection
d_isSplitSurjection_2138 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_752
d_isSplitSurjection_2138 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsSplitSurjection_752
d_isSplitSurjection_2138 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSplitSurjection_752
du_isSplitSurjection_2138 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isSplitSurjection_2138 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_752
du_isSplitSurjection_2138 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSplitSurjection_752
du_isSplitSurjection_2138 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSplitSurjection_752)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSplitSurjection_752
du_isSplitSurjection_1874 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2)
-- Function.Bundles._.SplitSurjection.isSurjection
d_isSurjection_2140 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
d_isSurjection_2140 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsSurjection_162
d_isSurjection_2140 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSurjection_162
du_isSurjection_2140 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isSurjection_2140 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
du_isSurjection_2140 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsSurjection_162
du_isSurjection_2140 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
MAlonzo.Code.Function.Structures.du_isSurjection_400
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
-- Function.Bundles._.SplitSurjection.strictlyInverseˡ
d_strictlyInverse'737'_2142 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_2142 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_2142 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2142 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_strictlyInverse'737'_2142 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2142 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2142 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_396
      ((T_LeftInverse_1792 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_from_1806 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2))
-- Function.Bundles._.SplitSurjection.surjection
d_surjection_2144 ::
  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 ->
  T_LeftInverse_1792 -> T_Surjection_846
d_surjection_2144 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Surjection_846
d_surjection_2144 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_LeftInverse_1792 -> T_Surjection_846
du_surjection_2144 T_LeftInverse_1792
v6
du_surjection_2144 :: T_LeftInverse_1792 -> T_Surjection_846
du_surjection_2144 :: T_LeftInverse_1792 -> T_Surjection_846
du_surjection_2144 T_LeftInverse_1792
v0 = (T_LeftInverse_1792 -> T_Surjection_846)
-> AgdaAny -> T_Surjection_846
forall a b. a -> b
coe T_LeftInverse_1792 -> T_Surjection_846
du_surjection_1876 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)
-- Function.Bundles._.SplitSurjection.to
d_to_2146 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_to_2146 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_to_2146 T_LeftInverse_1792
v0 = (T_LeftInverse_1792 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_to_1804 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)
-- Function.Bundles._.SplitSurjection.to-cong
d_to'45'cong_2148 ::
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2148 :: T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2148 T_LeftInverse_1792
v0 = (T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1808 (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v0)
-- Function.Bundles._.SplitSurjection.Eq₁._≈_
d__'8776'__2152 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2152 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2152 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₁._≉_
d__'8777'__2154 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2154 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2154 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₁.Carrier
d_Carrier_2156 ::
  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 ->
  T_LeftInverse_1792 -> ()
d_Carrier_2156 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
d_Carrier_2156 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₁.isEquivalence
d_isEquivalence_2158 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2158 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsEquivalence_26
d_isEquivalence_2158 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_2158 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isEquivalence_2158 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2158 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_2158 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4)))
-- Function.Bundles._.SplitSurjection.Eq₁.isPartialEquivalence
d_isPartialEquivalence_2160 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2160 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2160 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2160 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isPartialEquivalence_2160 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2160 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2160 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₁.partialSetoid
d_partialSetoid_2162 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_PartialSetoid_10
d_partialSetoid_2162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_2162 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_partialSetoid_2162 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2162 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_2162 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.SplitSurjection.Eq₁.refl
d_refl_2164 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_refl_2164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
d_refl_2164 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_2164 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_refl_2164 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_2164 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_2164 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.SplitSurjection.Eq₁.reflexive
d_reflexive_2166 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2166 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_reflexive_2166 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2166 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2166 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.SplitSurjection.Eq₁.setoid
d_setoid_2168 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2168 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Setoid_44
d_setoid_2168 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_2168 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_setoid_2168 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2168 :: T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_2168 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.SplitSurjection.Eq₁.sym
d_sym_2170 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2170 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2170 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_sym_2170 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2170 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2170 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₁.trans
d_trans_2172 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2172 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2172 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2172 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_trans_2172 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2172 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2172 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₂._≈_
d__'8776'__2176 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2176 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2176 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₂._≉_
d__'8777'__2178 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2178 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2178 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₂.Carrier
d_Carrier_2180 ::
  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 ->
  T_LeftInverse_1792 -> ()
d_Carrier_2180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
d_Carrier_2180 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₂.isEquivalence
d_isEquivalence_2182 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2182 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsEquivalence_26
d_isEquivalence_2182 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_2182 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isEquivalence_2182 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2182 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsEquivalence_26
du_isEquivalence_2182 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4)))
-- Function.Bundles._.SplitSurjection.Eq₂.isPartialEquivalence
d_isPartialEquivalence_2184 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2184 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2184 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2184 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_isPartialEquivalence_2184 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2184 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2184 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₂.partialSetoid
d_partialSetoid_2186 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2186 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_PartialSetoid_10
d_partialSetoid_2186 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_2186 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_partialSetoid_2186 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2186 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_PartialSetoid_10
du_partialSetoid_2186 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
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
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.SplitSurjection.Eq₂.refl
d_refl_2188 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
d_refl_2188 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
d_refl_2188 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_2188 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_refl_2188 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_2188 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> AgdaAny -> AgdaAny
du_refl_2188 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       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_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.SplitSurjection.Eq₂.reflexive
d_reflexive_2190 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2190 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_reflexive_2190 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2190 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2190 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
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_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
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.SplitSurjection.Eq₂.setoid
d_setoid_2192 ::
  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 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> T_Setoid_44
d_setoid_2192 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_2192 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_setoid_2192 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2192 :: T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_Setoid_44
du_setoid_2192 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.SplitSurjection.Eq₂.sym
d_sym_2194 ::
  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 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2194 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2194 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_sym_2194 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2194 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2194 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₂.trans
d_trans_2196 ::
  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 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2196 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2196 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2196 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_1792
v6
du_trans_2196 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_1792 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2196 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_1792
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2196 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_1792
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_1792 -> T_IsLeftInverse_322
du_isLeftInverse_1816 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_1792 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1792
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_322 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_334 (AgdaAny -> T_IsLeftInverse_322
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4) 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
v5)))))
-- Function.Bundles._⟶ₛ_
d__'10230''8347'__2198 ::
  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__'10230''8347'__2198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
d__'10230''8347'__2198 = 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.Bundles._⟶_
d__'10230'__2200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'10230'__2200 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'10230'__2200 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↣_
d__'8611'__2206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8611'__2206 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8611'__2206 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↠_
d__'8608'__2212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8608'__2212 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8608'__2212 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._⤖_
d__'10518'__2218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'10518'__2218 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'10518'__2218 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._⇔_
d__'8660'__2224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8660'__2224 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8660'__2224 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↩_
d__'8617'__2230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8617'__2230 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8617'__2230 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↪_
d__'8618'__2236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8618'__2236 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8618'__2236 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↩↪_
d__'8617''8618'__2242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8617''8618'__2242 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8617''8618'__2242 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↔_
d__'8596'__2248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8596'__2248 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8596'__2248 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._.mk⟶
d_mk'10230'_2266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> () -> (AgdaAny -> AgdaAny) -> T_Func_714
d_mk'10230'_2266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Func_714
d_mk'10230'_2266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 = (AgdaAny -> AgdaAny) -> T_Func_714
du_mk'10230'_2266 AgdaAny -> AgdaAny
v4
du_mk'10230'_2266 :: (AgdaAny -> AgdaAny) -> T_Func_714
du_mk'10230'_2266 :: (AgdaAny -> AgdaAny) -> T_Func_714
du_mk'10230'_2266 AgdaAny -> AgdaAny
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714)
-> AgdaAny -> AgdaAny -> T_Func_714
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_714
C_Func'46'constructor_6307 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased
-- Function.Bundles._.mk↣
d_mk'8611'_2272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Injection_776
d_mk'8611'_2272 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_776
d_mk'8611'_2272 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v5 = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_776
du_mk'8611'_2272 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v5
du_mk'8611'_2272 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Injection_776
du_mk'8611'_2272 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_776
du_mk'8611'_2272 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Injection_776)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Injection_776
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Injection_776
C_Injection'46'constructor_8675 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased ((AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v1)
-- Function.Bundles._.mk↠
d_mk'8608'_2280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_846
d_mk'8608'_2280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_846
d_mk'8608'_2280 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5 = (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_846
du_mk'8608'_2280 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5
du_mk'8608'_2280 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_846
du_mk'8608'_2280 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_846
du_mk'8608'_2280 AgdaAny -> AgdaAny
v0 AgdaAny -> T_Σ_14
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_846)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_846
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_846
C_Surjection'46'constructor_11197 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased ((AgdaAny -> T_Σ_14) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v1)
-- Function.Bundles._.mk⤖
d_mk'10518'_2288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Bijection_926
d_mk'10518'_2288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Bijection_926
d_mk'10518'_2288 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 T_Σ_14
v5 = (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Bijection_926
du_mk'10518'_2288 AgdaAny -> AgdaAny
v4 T_Σ_14
v5
du_mk'10518'_2288 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Bijection_926
du_mk'10518'_2288 :: (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Bijection_926
du_mk'10518'_2288 AgdaAny -> AgdaAny
v0 T_Σ_14
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Bijection_926)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Bijection_926
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Bijection_926
C_Bijection'46'constructor_15277 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased (T_Σ_14 -> AgdaAny
forall a b. a -> b
coe T_Σ_14
v1)
-- Function.Bundles._.mk⇔
d_mk'8660'_2298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_1714
d_mk'8660'_2298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Equivalence_1714
d_mk'8660'_2298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 = (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_1714
du_mk'8660'_2298 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5
du_mk'8660'_2298 ::
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_1714
du_mk'8660'_2298 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_1714
du_mk'8660'_2298 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_1714)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_1714
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_1714
C_Equivalence'46'constructor_25797 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
-- Function.Bundles._.mk↩
d_mk'8617'_2308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_LeftInverse_1792
d_mk'8617'_2308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_LeftInverse_1792
d_mk'8617'_2308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v6
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_LeftInverse_1792
du_mk'8617'_2308 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v6
du_mk'8617'_2308 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_LeftInverse_1792
du_mk'8617'_2308 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_LeftInverse_1792
du_mk'8617'_2308 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v2
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_LeftInverse_1792)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_LeftInverse_1792
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1792
C_LeftInverse'46'constructor_29775 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
      ((AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v2)
-- Function.Bundles._.mk↪
d_mk'8618'_2320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_RightInverse_1880
d_mk'8618'_2320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_RightInverse_1880
d_mk'8618'_2320 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v6
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_RightInverse_1880
du_mk'8618'_2320 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v6
du_mk'8618'_2320 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_RightInverse_1880
du_mk'8618'_2320 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_RightInverse_1880
du_mk'8618'_2320 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v2
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_RightInverse_1880)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_RightInverse_1880
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_RightInverse_1880
C_RightInverse'46'constructor_34573 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
      ((AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v2)
-- Function.Bundles._.mk↩↪
d_mk'8617''8618'_2334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_BiInverse_2080
d_mk'8617''8618'_2334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_BiInverse_2080
d_mk'8617''8618'_2334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v7 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v8
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_BiInverse_2080
du_mk'8617''8618'_2334 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v7 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v8
du_mk'8617''8618'_2334 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_BiInverse_2080
du_mk'8617''8618'_2334 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_BiInverse_2080
du_mk'8617''8618'_2334 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v3 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v4
  = ((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)
 -> T_BiInverse_2080)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_BiInverse_2080
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 -> AgdaAny -> AgdaAny)
-> T_BiInverse_2080
C_BiInverse'46'constructor_47439 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) AgdaAny
forall a. a
erased
      AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased ((AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v3) ((AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v4)
-- Function.Bundles._.mk↔
d_mk'8596'_2350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Inverse_1960
d_mk'8596'_2350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Inverse_1960
d_mk'8596'_2350 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_Σ_14
v6
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1960
du_mk'8596'_2350 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_Σ_14
v6
du_mk'8596'_2350 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Inverse_1960
du_mk'8596'_2350 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1960
du_mk'8596'_2350 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_Σ_14
v2
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Inverse_1960)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_Inverse_1960
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Inverse_1960
C_Inverse'46'constructor_38621 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
      (T_Σ_14 -> AgdaAny
forall a b. a -> b
coe T_Σ_14
v2)
-- Function.Bundles._.mk↠ₛ
d_mk'8608''8347'_2360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_846
d_mk'8608''8347'_2360 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_846
d_mk'8608''8347'_2360 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5
  = (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_846
du_mk'8608''8347'_2360 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5
du_mk'8608''8347'_2360 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_846
du_mk'8608''8347'_2360 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_846
du_mk'8608''8347'_2360 AgdaAny -> AgdaAny
v0 AgdaAny -> T_Σ_14
v1
  = ((AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_846)
-> AgdaAny -> AgdaAny -> T_Surjection_846
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_846
du_mk'8608'_2280 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0)
      (((AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14)
-> (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Consequences.Propositional.du_strictlySurjective'8658'surjective_40
         AgdaAny -> AgdaAny
v0 AgdaAny -> T_Σ_14
v1)
-- Function.Bundles._.mk↔ₛ′
d_mk'8596''8347''8242'_2366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Inverse_1960
d_mk'8596''8347''8242'_2366 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> (AgdaAny -> T__'8801'__12)
-> T_Inverse_1960
d_mk'8596''8347''8242'_2366 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 ~AgdaAny -> T__'8801'__12
v6 ~AgdaAny -> T__'8801'__12
v7
  = (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Inverse_1960
du_mk'8596''8347''8242'_2366 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5
du_mk'8596''8347''8242'_2366 ::
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Inverse_1960
du_mk'8596''8347''8242'_2366 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Inverse_1960
du_mk'8596''8347''8242'_2366 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1960)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Inverse_1960
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1960
du_mk'8596'_2350 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
      ((AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased)
-- Function.Bundles._._⟨$⟩_
d__'10216''36''10217'__2392 :: T_Func_714 -> AgdaAny -> AgdaAny
d__'10216''36''10217'__2392 :: T_Func_714 -> AgdaAny -> AgdaAny
d__'10216''36''10217'__2392 T_Func_714
v0 = (T_Func_714 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Func_714 -> AgdaAny -> AgdaAny
d_to_720 (T_Func_714 -> AgdaAny
forall a b. a -> b
coe T_Func_714
v0)