{-# 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.Bundles.Raw
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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__30 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__30 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> 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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 -> ()
d_Carrier_32 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
d_Carrier_32 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection
d_IsBijection_50 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBijection_50 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsCongruent
d_IsCongruent_54 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCongruent_54 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsInjection
d_IsInjection_58 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInjection_58 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsSurjection
d_IsSurjection_78 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSurjection_78 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsBijection.isInjection
d_isInjection_232 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_98
d_isInjection_232 :: T_IsBijection_256 -> T_IsInjection_98
d_isInjection_232 T_IsBijection_256
v0
  = (T_IsBijection_256 -> T_IsInjection_98)
-> AgdaAny -> T_IsInjection_98
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0)
-- Function.Bundles._._.IsBijection.surjective
d_surjective_238 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_238 :: T_IsBijection_256 -> AgdaAny -> T_Σ_14
d_surjective_238 T_IsBijection_256
v0
  = (T_IsBijection_256 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsBijection_256 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.d_surjective_266 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0)
-- Function.Bundles._._.IsBijection.Eq₁._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__242 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__244 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 -> ()
d_Carrier_246 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Level_18
d_Carrier_246 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_248 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsEquivalence_28
d_isEquivalence_248 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_248 T_IsBijection_256
v7
du_isEquivalence_248 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_248 :: T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_248 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_250 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_250 T_IsBijection_256
v7
du_isPartialEquivalence_250 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_250 :: T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_250 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsBijection.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_PartialSetoid_10
d_partialSetoid_252 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_252 T_IsBijection_256
v7
du_partialSetoid_252 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_252 :: T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_252 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
d_rawSetoid_254 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny
d_refl_256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
d_refl_256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_256 T_IsBijection_256
v7
du_refl_256 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny
du_refl_256 :: T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_256 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_258 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_258 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_258 T_IsBijection_256
v7
du_reflexive_258 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_258 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_258 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsBijection.Eq₁.setoid
d_setoid_260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_260 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Setoid_46
d_setoid_260 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256 -> T_Setoid_46
du_setoid_260 T_IsBijection_256
v7
du_setoid_260 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_260 :: T_IsBijection_256 -> T_Setoid_46
du_setoid_260 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v1)))
-- Function.Bundles._._.IsBijection.Eq₁.sym
d_sym_262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_262 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_262 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_262 T_IsBijection_256
v7
du_sym_262 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_262 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_262 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsBijection.Eq₁.trans
d_trans_264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_264 T_IsBijection_256
v7
du_trans_264 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_264 :: T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_264 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsBijection.Eq₂._≈_
d__'8776'__268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__268 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__270 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 -> ()
d_Carrier_272 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Level_18
d_Carrier_272 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_274 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsEquivalence_28
d_isEquivalence_274 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_274 T_IsBijection_256
v7
du_isEquivalence_274 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_274 :: T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_274 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_276 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_276 T_IsBijection_256
v7
du_isPartialEquivalence_276 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_276 :: T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_276 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsBijection.Eq₂.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_278 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_PartialSetoid_10
d_partialSetoid_278 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_278 T_IsBijection_256
v7
du_partialSetoid_278 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_278 :: T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_278 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₂.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
d_rawSetoid_280 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny
d_refl_282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
d_refl_282 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_282 T_IsBijection_256
v7
du_refl_282 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny
du_refl_282 :: T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_282 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  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_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> 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_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7
  = T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_284 T_IsBijection_256
v7
du_reflexive_284 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_284 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_284 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsBijection.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Setoid_46
d_setoid_286 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256 -> T_Setoid_46
du_setoid_286 T_IsBijection_256
v7
du_setoid_286 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_286 :: T_IsBijection_256 -> T_Setoid_46
du_setoid_286 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v1)))
-- Function.Bundles._._.IsBijection.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> 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_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_288 T_IsBijection_256
v7
du_sym_288 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_288 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_288 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsBijection.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> 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_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_256
v7 = T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_290 T_IsBijection_256
v7
du_trans_290 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_290 :: T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_290 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1
          = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsCongruent.cong
d_cong_294 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_294 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_294 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'_296 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_296 :: T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_296 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
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'_298 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_298 :: T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_298 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
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'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__302 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__302 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₁._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__304 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₁.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 -> ()
d_Carrier_306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
d_Carrier_306 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₁.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_28
d_isEquivalence_308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsEquivalence_28
du_isEquivalence_308 T_IsCongruent_22
v7
du_isEquivalence_308 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_308 :: T_IsCongruent_22 -> T_IsEquivalence_28
du_isEquivalence_308 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_310 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_310 T_IsCongruent_22
v7
du_isPartialEquivalence_310 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_310 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_310 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Bundles._._.IsCongruent.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_312 T_IsCongruent_22
v7
du_partialSetoid_312 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_312 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_312 T_IsCongruent_22
v0
  = (T_Setoid_46 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
d_rawSetoid_314 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₁.refl
d_refl_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
d_refl_316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_316 T_IsCongruent_22
v7
du_refl_316 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
du_refl_316 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_316 T_IsCongruent_22
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
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_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_318 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_318 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_318 T_IsCongruent_22
v7
du_reflexive_318 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_318 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_318 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
           AgdaAny
v2)
-- Function.Bundles._._.IsCongruent.Eq₁.setoid
d_setoid_320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_46
d_setoid_320 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 = (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_46
du_setoid_320
du_setoid_320 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_320 :: (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_46
du_setoid_320 AgdaAny -> AgdaAny
v0 T_IsCongruent_22
v1
  = (T_IsCongruent_22 -> T_Setoid_46)
-> T_IsCongruent_22 -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 T_IsCongruent_22
v1
-- Function.Bundles._._.IsCongruent.Eq₁.sym
d_sym_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_322 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_322 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_322 T_IsCongruent_22
v7
du_sym_322 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_322 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_322 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Bundles._._.IsCongruent.Eq₁.trans
d_trans_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_324 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_324 T_IsCongruent_22
v7
du_trans_324 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_324 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_324 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Bundles._._.IsCongruent.Eq₂._≈_
d__'8776'__328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__328 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂._≉_
d__'8777'__330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__330 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂.Carrier
d_Carrier_332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 -> ()
d_Carrier_332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
d_Carrier_332 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂.isEquivalence
d_isEquivalence_334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_28
d_isEquivalence_334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsEquivalence_28
du_isEquivalence_334 T_IsCongruent_22
v7
du_isEquivalence_334 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_334 :: T_IsCongruent_22 -> T_IsEquivalence_28
du_isEquivalence_334 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
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_336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_336 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_336 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_336 T_IsCongruent_22
v7
du_isPartialEquivalence_336 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_336 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_336 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Bundles._._.IsCongruent.Eq₂.partialSetoid
d_partialSetoid_338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_338 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_338 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_338 T_IsCongruent_22
v7
du_partialSetoid_338 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_338 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_338 T_IsCongruent_22
v0
  = (T_Setoid_46 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₂.rawSetoid
d_rawSetoid_340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
d_rawSetoid_340 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂.refl
d_refl_342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
d_refl_342 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_342 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_342 T_IsCongruent_22
v7
du_refl_342 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
du_refl_342 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_342 T_IsCongruent_22
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
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_344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_344 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsCongruent_22
v7
du_reflexive_344 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_344 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
           AgdaAny
v2)
-- Function.Bundles._._.IsCongruent.Eq₂.setoid
d_setoid_346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_46
d_setoid_346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 = (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_46
du_setoid_346
du_setoid_346 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_346 :: (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_46
du_setoid_346 AgdaAny -> AgdaAny
v0 T_IsCongruent_22
v1
  = (T_IsCongruent_22 -> T_Setoid_46)
-> T_IsCongruent_22 -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 T_IsCongruent_22
v1
-- Function.Bundles._._.IsCongruent.Eq₂.sym
d_sym_348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_348 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_348 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_348 T_IsCongruent_22
v7
du_sym_348 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_348 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_348 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Bundles._._.IsCongruent.Eq₂.trans
d_trans_350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_350 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_350 T_IsCongruent_22
v7
du_trans_350 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_350 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_350 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1
          = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Bundles._._.IsInjection.injective
d_injective_356 ::
  MAlonzo.Code.Function.Structures.T_IsInjection_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_356 :: T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_356 T_IsInjection_98
v0
  = (T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_injective_108 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v0)
-- Function.Bundles._._.IsInjection.isCongruent
d_isCongruent_358 ::
  MAlonzo.Code.Function.Structures.T_IsInjection_98 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_358 :: T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_358 T_IsInjection_98
v0
  = (T_IsInjection_98 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v0)
-- Function.Bundles._._.IsSurjection.isCongruent
d_isCongruent_712 ::
  MAlonzo.Code.Function.Structures.T_IsSurjection_174 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_712 :: T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_712 T_IsSurjection_174
v0
  = (T_IsSurjection_174 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsSurjection_174 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_182 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0)
-- Function.Bundles._._.IsSurjection.strictlySurjective
d_strictlySurjective_718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_718 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_718 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5
  = (AgdaAny -> AgdaAny) -> T_IsSurjection_174 -> AgdaAny -> T_Σ_14
du_strictlySurjective_718
du_strictlySurjective_718 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_718 :: (AgdaAny -> AgdaAny) -> T_IsSurjection_174 -> AgdaAny -> T_Σ_14
du_strictlySurjective_718 AgdaAny -> AgdaAny
v0 T_IsSurjection_174
v1 AgdaAny
v2
  = (T_IsSurjection_174 -> AgdaAny -> T_Σ_14)
-> T_IsSurjection_174 -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSurjection_174 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_246 T_IsSurjection_174
v1 AgdaAny
v2
-- Function.Bundles._._.IsSurjection.surjective
d_surjective_720 ::
  MAlonzo.Code.Function.Structures.T_IsSurjection_174 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_720 :: T_IsSurjection_174 -> AgdaAny -> T_Σ_14
d_surjective_720 T_IsSurjection_174
v0
  = (T_IsSurjection_174 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSurjection_174 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.d_surjective_184 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0)
-- Function.Bundles._.Func
d_Func_774 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Func_774 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Func_774
  = C_constructor_840 (AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Func.to
d_to_780 :: T_Func_774 -> AgdaAny -> AgdaAny
d_to_780 :: T_Func_774 -> AgdaAny -> AgdaAny
d_to_780 T_Func_774
v0
  = case T_Func_774 -> T_Func_774
forall a b. a -> b
coe T_Func_774
v0 of
      C_constructor_840 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Func_774
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Func.cong
d_cong_782 ::
  T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_782 :: T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_782 T_Func_774
v0
  = case T_Func_774 -> T_Func_774
forall a b. a -> b
coe T_Func_774
v0 of
      C_constructor_840 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_774
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Func.isCongruent
d_isCongruent_784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_IsCongruent_22
d_isCongruent_784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_isCongruent_784 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_784 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_constructor_94
      ((T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_782 (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1))
-- Function.Bundles._.Func._.Eq₁._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> ()
d__'8776'__790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__790 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁._≉_
d__'8777'__792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> ()
d__'8777'__792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__792 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> ()
d_Carrier_794 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_Level_18
d_Carrier_794 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁.isEquivalence
d_isEquivalence_796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_796 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_IsEquivalence_28
d_isEquivalence_796 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsEquivalence_28
du_isEquivalence_796 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_isEquivalence_796 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_796 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsEquivalence_28
du_isEquivalence_796 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
-- Function.Bundles._.Func._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_798 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_798 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Func_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_798 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_isPartialEquivalence_798 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_798 :: T_Setoid_46
-> T_Setoid_46 -> T_Func_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_798 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Func._.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_PartialSetoid_10
d_partialSetoid_800 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_PartialSetoid_10
du_partialSetoid_800 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_partialSetoid_800 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_800 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_PartialSetoid_10
du_partialSetoid_800 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Func._.Eq₁.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_RawSetoid_12
d_rawSetoid_802 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny
d_refl_804 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
d_refl_804 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> AgdaAny -> AgdaAny
du_refl_804 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_refl_804 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny
du_refl_804 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> AgdaAny -> AgdaAny
du_refl_804 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Func._.Eq₁.reflexive
d_reflexive_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_806 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_reflexive_806 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_806 :: T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_806 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
              AgdaAny
v5))
-- Function.Bundles._.Func._.Eq₁.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_Setoid_46
d_setoid_808 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_Setoid_46
du_setoid_808 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_setoid_808 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_808 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_Setoid_46
du_setoid_808 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2))
-- Function.Bundles._.Func._.Eq₁.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_810 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_810 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_810 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_sym_810 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_810 :: T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_810 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Func._.Eq₁.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_812 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_812 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_trans_812 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_812 :: T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_812 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Func._.Eq₂._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> ()
d__'8776'__816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__816 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₂._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> ()
d__'8777'__818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__818 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₂.Carrier
d_Carrier_820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> ()
d_Carrier_820 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_Level_18
d_Carrier_820 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₂.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_822 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_IsEquivalence_28
d_isEquivalence_822 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsEquivalence_28
du_isEquivalence_822 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_isEquivalence_822 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_822 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsEquivalence_28
du_isEquivalence_822 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
-- Function.Bundles._.Func._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Func_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_824 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_isPartialEquivalence_824 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_824 :: T_Setoid_46
-> T_Setoid_46 -> T_Func_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_824 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Func._.Eq₂.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_PartialSetoid_10
d_partialSetoid_826 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_PartialSetoid_10
du_partialSetoid_826 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_partialSetoid_826 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_826 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_PartialSetoid_10
du_partialSetoid_826 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Func._.Eq₂.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_828 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_RawSetoid_12
d_rawSetoid_828 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Func._.Eq₂.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny
d_refl_830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
d_refl_830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> AgdaAny -> AgdaAny
du_refl_830 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_refl_830 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny
du_refl_830 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> AgdaAny -> AgdaAny
du_refl_830 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Func._.Eq₂.reflexive
d_reflexive_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_832 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_reflexive_832 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_832 :: T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_832 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
              AgdaAny
v5))
-- Function.Bundles._.Func._.Eq₂.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> T_Setoid_46
d_setoid_834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_Setoid_46
du_setoid_834 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_setoid_834 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_834 :: T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_Setoid_46
du_setoid_834 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
      ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2))
-- Function.Bundles._.Func._.Eq₂.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_836 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_836 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_sym_836 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_836 :: T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_836 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Func._.Eq₂.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_838 T_Setoid_46
v4 T_Setoid_46
v5 T_Func_774
v6
du_trans_838 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Func_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_838 :: T_Setoid_46
-> T_Setoid_46
-> T_Func_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_838 T_Setoid_46
v0 T_Setoid_46
v1 T_Func_774
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Injection
d_Injection_842 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Injection_842 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Injection_842
  = C_constructor_916 (AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Injection.to
d_to_850 :: T_Injection_842 -> AgdaAny -> AgdaAny
d_to_850 :: T_Injection_842 -> AgdaAny -> AgdaAny
d_to_850 T_Injection_842
v0
  = case T_Injection_842 -> T_Injection_842
forall a b. a -> b
coe T_Injection_842
v0 of
      C_constructor_916 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_842
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.cong
d_cong_852 ::
  T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 :: T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 T_Injection_842
v0
  = case T_Injection_842 -> T_Injection_842
forall a b. a -> b
coe T_Injection_842
v0 of
      C_constructor_916 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_842
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.injective
d_injective_854 ::
  T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_854 :: T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_854 T_Injection_842
v0
  = case T_Injection_842 -> T_Injection_842
forall a b. a -> b
coe T_Injection_842
v0 of
      C_constructor_916 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_842
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.function
d_function_856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> T_Func_774
d_function_856 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_Func_774
d_function_856 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Injection_842
v6 = T_Injection_842 -> T_Func_774
du_function_856 T_Injection_842
v6
du_function_856 :: T_Injection_842 -> T_Func_774
du_function_856 :: T_Injection_842 -> T_Func_774
du_function_856 T_Injection_842
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774)
-> AgdaAny -> AgdaAny -> T_Func_774
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774
C_constructor_840 ((T_Injection_842 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> AgdaAny -> AgdaAny
d_to_850 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v0)) ((T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v0))
-- Function.Bundles._.Injection._.isCongruent
d_isCongruent_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_860 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_IsCongruent_22
d_isCongruent_860 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsCongruent_22
du_isCongruent_860 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_isCongruent_860 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_860 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsCongruent_22
du_isCongruent_860 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) ((T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2))
-- Function.Bundles._.Injection._.Eq₁._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> ()
d__'8776'__864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__864 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁._≉_
d__'8777'__866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> ()
d__'8777'__866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__866 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> ()
d_Carrier_868 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_Level_18
d_Carrier_868 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_870 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_IsEquivalence_28
d_isEquivalence_870 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsEquivalence_28
du_isEquivalence_870 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_isEquivalence_870 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_870 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsEquivalence_28
du_isEquivalence_870 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
-- Function.Bundles._.Injection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_872 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Injection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_872 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_isPartialEquivalence_872 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_872 :: T_Setoid_46
-> T_Setoid_46 -> T_Injection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_872 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Injection._.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_PartialSetoid_10
d_partialSetoid_874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_PartialSetoid_10
du_partialSetoid_874 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_partialSetoid_874 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_874 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_PartialSetoid_10
du_partialSetoid_874 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Injection._.Eq₁.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_RawSetoid_12
d_rawSetoid_876 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny
d_refl_878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
d_refl_878 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> AgdaAny -> AgdaAny
du_refl_878 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_refl_878 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny
du_refl_878 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> AgdaAny -> AgdaAny
du_refl_878 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Injection._.Eq₁.reflexive
d_reflexive_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_880 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_880 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_reflexive_880 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_880 :: T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_880 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Injection._.Eq₁.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_Setoid_46
d_setoid_882 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_Setoid_46
du_setoid_882 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_setoid_882 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_882 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_Setoid_46
du_setoid_882 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Injection._.Eq₁.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_884 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_sym_884 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_884 :: T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_884 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Injection._.Eq₁.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_886 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_trans_886 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_886 :: T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_886 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Injection._.Eq₂._≈_
d__'8776'__890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> ()
d__'8776'__890 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__890 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> ()
d__'8777'__892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__892 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> ()
d_Carrier_894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_Level_18
d_Carrier_894 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_IsEquivalence_28
d_isEquivalence_896 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsEquivalence_28
du_isEquivalence_896 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_isEquivalence_896 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_896 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsEquivalence_28
du_isEquivalence_896 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
-- Function.Bundles._.Injection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Injection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_898 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_isPartialEquivalence_898 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_898 :: T_Setoid_46
-> T_Setoid_46 -> T_Injection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_898 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Injection._.Eq₂.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_PartialSetoid_10
d_partialSetoid_900 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_PartialSetoid_10
du_partialSetoid_900 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_partialSetoid_900 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_900 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_PartialSetoid_10
du_partialSetoid_900 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Injection._.Eq₂.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_RawSetoid_12
d_rawSetoid_902 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Injection._.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny
d_refl_904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
d_refl_904 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> AgdaAny -> AgdaAny
du_refl_904 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_refl_904 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny
du_refl_904 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> AgdaAny -> AgdaAny
du_refl_904 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Injection._.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  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_46
-> T_Setoid_46
-> T_Injection_842
-> 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_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_906 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_reflexive_906 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_906 :: T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_906 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Injection._.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_Setoid_46
d_setoid_908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_Setoid_46
du_setoid_908 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_setoid_908 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_908 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_Setoid_46
du_setoid_908 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Injection._.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> 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_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_910 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_sym_910 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_910 :: T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_910 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Injection._.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> 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_46
v4 T_Setoid_46
v5 T_Injection_842
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_912 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_trans_912 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_912 :: T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_912 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = let v3 :: AgdaAny
v3 = (T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Injection.isInjection
d_isInjection_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_98
d_isInjection_914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Injection_842
-> T_IsInjection_98
d_isInjection_914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsInjection_98
du_isInjection_914 T_Setoid_46
v4 T_Setoid_46
v5 T_Injection_842
v6
du_isInjection_914 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Injection_842 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_98
du_isInjection_914 :: T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsInjection_98
du_isInjection_914 T_Setoid_46
v0 T_Setoid_46
v1 T_Injection_842
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInjection_98)
-> AgdaAny -> AgdaAny -> T_IsInjection_98
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInjection_98
MAlonzo.Code.Function.Structures.C_constructor_170
      ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
         ((T_Injection_842 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> T_Func_774
du_function_856 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2)))
      ((T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_854 (T_Injection_842 -> AgdaAny
forall a b. a -> b
coe T_Injection_842
v2))
-- Function.Bundles._.Surjection
d_Surjection_918 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Surjection_918 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Surjection_918
  = C_constructor_1002 (AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Bundles._.Surjection.to
d_to_926 :: T_Surjection_918 -> AgdaAny -> AgdaAny
d_to_926 :: T_Surjection_918 -> AgdaAny -> AgdaAny
d_to_926 T_Surjection_918
v0
  = case T_Surjection_918 -> T_Surjection_918
forall a b. a -> b
coe T_Surjection_918
v0 of
      C_constructor_1002 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_918
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.cong
d_cong_928 ::
  T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_928 :: T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_928 T_Surjection_918
v0
  = case T_Surjection_918 -> T_Surjection_918
forall a b. a -> b
coe T_Surjection_918
v0 of
      C_constructor_1002 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_918
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.surjective
d_surjective_930 ::
  T_Surjection_918 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_930 :: T_Surjection_918 -> AgdaAny -> T_Σ_14
d_surjective_930 T_Surjection_918
v0
  = case T_Surjection_918 -> T_Surjection_918
forall a b. a -> b
coe T_Surjection_918
v0 of
      C_constructor_1002 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_918
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.function
d_function_932 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> T_Func_774
d_function_932 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_Func_774
d_function_932 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Surjection_918
v6 = T_Surjection_918 -> T_Func_774
du_function_932 T_Surjection_918
v6
du_function_932 :: T_Surjection_918 -> T_Func_774
du_function_932 :: T_Surjection_918 -> T_Func_774
du_function_932 T_Surjection_918
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774)
-> AgdaAny -> AgdaAny -> T_Func_774
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774
C_constructor_840 ((T_Surjection_918 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> AgdaAny -> AgdaAny
d_to_926 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v0)) ((T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_928 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v0))
-- Function.Bundles._.Surjection._.isCongruent
d_isCongruent_936 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_936 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_IsCongruent_22
d_isCongruent_936 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> T_IsCongruent_22
du_isCongruent_936 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_isCongruent_936 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_936 :: T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> T_IsCongruent_22
du_isCongruent_936 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) ((T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2))
-- Function.Bundles._.Surjection._.Eq₁._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> ()
d__'8776'__940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__940 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> ()
d__'8777'__942 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__942 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> ()
d_Carrier_944 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_Level_18
d_Carrier_944 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_IsEquivalence_28
d_isEquivalence_946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsEquivalence_28
du_isEquivalence_946 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_isEquivalence_946 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_946 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsEquivalence_28
du_isEquivalence_946 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
-- Function.Bundles._.Surjection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_948 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_isPartialEquivalence_948 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_948 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_948 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Surjection._.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_950 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_PartialSetoid_10
d_partialSetoid_950 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_PartialSetoid_10
du_partialSetoid_950 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_partialSetoid_950 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_950 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_PartialSetoid_10
du_partialSetoid_950 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Surjection._.Eq₁.rawSetoid
d_rawSetoid_952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_952 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_RawSetoid_12
d_rawSetoid_952 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny
d_refl_954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
d_refl_954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> AgdaAny
du_refl_954 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_refl_954 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny
du_refl_954 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> AgdaAny
du_refl_954 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Surjection._.Eq₁.reflexive
d_reflexive_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_956 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_956 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_956 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_reflexive_956 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_956 :: T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_956 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Surjection._.Eq₁.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_Setoid_46
d_setoid_958 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> T_Setoid_46
du_setoid_958 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_setoid_958 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_958 :: T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> T_Setoid_46
du_setoid_958 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Surjection._.Eq₁.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_960 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_960 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_960 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_sym_960 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_960 :: T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_960 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Surjection._.Eq₁.trans
d_trans_962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_962 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_962 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_962 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_trans_962 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_962 :: T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_962 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Surjection._.Eq₂._≈_
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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> ()
d__'8776'__966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__966 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂._≉_
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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> ()
d__'8777'__968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__968 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> ()
d_Carrier_970 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_Level_18
d_Carrier_970 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_972 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_IsEquivalence_28
d_isEquivalence_972 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsEquivalence_28
du_isEquivalence_972 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_isEquivalence_972 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_972 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsEquivalence_28
du_isEquivalence_972 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
-- Function.Bundles._.Surjection._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  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_46
-> T_Setoid_46
-> T_Surjection_918
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_974 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_isPartialEquivalence_974 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_974 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_974 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Surjection._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  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_46
-> T_Setoid_46
-> T_Surjection_918
-> T_PartialSetoid_10
d_partialSetoid_976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_PartialSetoid_10
du_partialSetoid_976 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_partialSetoid_976 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_976 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_PartialSetoid_10
du_partialSetoid_976 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Surjection._.Eq₂.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_RawSetoid_12
d_rawSetoid_978 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny
d_refl_980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
d_refl_980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> AgdaAny
du_refl_980 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_refl_980 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny
du_refl_980 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> AgdaAny
du_refl_980 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Surjection._.Eq₂.reflexive
d_reflexive_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_982 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_reflexive_982 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_982 :: T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_982 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Surjection._.Eq₂.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_Setoid_46
d_setoid_984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> T_Setoid_46
du_setoid_984 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_setoid_984 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_984 :: T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> T_Setoid_46
du_setoid_984 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Surjection._.Eq₂.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_986 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_sym_986 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_986 :: T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_986 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Surjection._.Eq₂.trans
d_trans_988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_988 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_trans_988 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_988 :: T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_988 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = let v3 :: AgdaAny
v3 = (T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Surjection.isSurjection
d_isSurjection_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
d_isSurjection_990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> T_IsSurjection_174
d_isSurjection_990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174
du_isSurjection_990 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_isSurjection_990 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
du_isSurjection_990 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174
du_isSurjection_990 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = (T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_174
MAlonzo.Code.Function.Structures.C_constructor_252
      ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
         ((T_Surjection_918 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> T_Func_774
du_function_932 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2)))
      ((T_Surjection_918 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> AgdaAny -> T_Σ_14
d_surjective_930 (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2))
-- Function.Bundles._.Surjection._.strictlySurjective
d_strictlySurjective_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> T_Σ_14
du_strictlySurjective_994 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6
du_strictlySurjective_994 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_994 :: T_Setoid_46 -> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> T_Σ_14
du_strictlySurjective_994 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
v2
  = (T_IsSurjection_174 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSurjection_174 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_246
      ((T_Setoid_46
 -> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174
du_isSurjection_990 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2))
-- Function.Bundles._.Surjection.to⁻
d_to'8315'_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny
d_to'8315'_996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
d_to'8315'_996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Surjection_918
v6 AgdaAny
v7
  = T_Surjection_918 -> AgdaAny -> AgdaAny
du_to'8315'_996 T_Surjection_918
v6 AgdaAny
v7
du_to'8315'_996 :: T_Surjection_918 -> AgdaAny -> AgdaAny
du_to'8315'_996 :: T_Surjection_918 -> AgdaAny -> AgdaAny
du_to'8315'_996 T_Surjection_918
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_918 -> AgdaAny -> T_Σ_14)
-> T_Surjection_918 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> AgdaAny -> T_Σ_14
d_surjective_930 T_Surjection_918
v0 AgdaAny
v1)
-- Function.Bundles._.Surjection.to∘to⁻
d_to'8728'to'8315'_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny
d_to'8728'to'8315'_1000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Surjection_918
-> AgdaAny
-> AgdaAny
d_to'8728'to'8315'_1000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 AgdaAny
v7
  = T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> AgdaAny
du_to'8728'to'8315'_1000 T_Setoid_46
v4 T_Setoid_46
v5 T_Surjection_918
v6 AgdaAny
v7
du_to'8728'to'8315'_1000 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Surjection_918 -> AgdaAny -> AgdaAny
du_to'8728'to'8315'_1000 :: T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> AgdaAny -> AgdaAny
du_to'8728'to'8315'_1000 T_Setoid_46
v0 T_Setoid_46
v1 T_Surjection_918
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_174 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSurjection_174 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_246
         ((T_Setoid_46
 -> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174
du_isSurjection_990 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Surjection_918 -> AgdaAny
forall a b. a -> b
coe T_Surjection_918
v2)) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
-- Function.Bundles._.Bijection
d_Bijection_1004 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Bijection_1004 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Bijection_1004
  = C_constructor_1094 (AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Function.Bundles._.Bijection.to
d_to_1012 :: T_Bijection_1004 -> AgdaAny -> AgdaAny
d_to_1012 :: T_Bijection_1004 -> AgdaAny -> AgdaAny
d_to_1012 T_Bijection_1004
v0
  = case T_Bijection_1004 -> T_Bijection_1004
forall a b. a -> b
coe T_Bijection_1004
v0 of
      C_constructor_1094 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_1004
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.cong
d_cong_1014 ::
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1014 :: T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1014 T_Bijection_1004
v0
  = case T_Bijection_1004 -> T_Bijection_1004
forall a b. a -> b
coe T_Bijection_1004
v0 of
      C_constructor_1094 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_1004
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.bijective
d_bijective_1016 ::
  T_Bijection_1004 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_bijective_1016 :: T_Bijection_1004 -> T_Σ_14
d_bijective_1016 T_Bijection_1004
v0
  = case T_Bijection_1004 -> T_Bijection_1004
forall a b. a -> b
coe T_Bijection_1004
v0 of
      C_constructor_1094 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_1004
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.injective
d_injective_1018 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1018 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_injective_1018 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Bijection_1004
v6 AgdaAny
v7 AgdaAny
v8
  = T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_1018 T_Bijection_1004
v6 AgdaAny
v7 AgdaAny
v8
du_injective_1018 ::
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_1018 :: T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_1018 T_Bijection_1004
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_1004 -> T_Σ_14
d_bijective_1016 (T_Bijection_1004 -> T_Bijection_1004
forall a b. a -> b
coe T_Bijection_1004
v0)) AgdaAny
v1 AgdaAny
v2
-- Function.Bundles._.Bijection.surjective
d_surjective_1020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> T_Σ_14
d_surjective_1020 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Bijection_1004 -> AgdaAny -> T_Σ_14
du_surjective_1020 T_Bijection_1004
v6
du_surjective_1020 ::
  T_Bijection_1004 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_surjective_1020 :: T_Bijection_1004 -> AgdaAny -> T_Σ_14
du_surjective_1020 T_Bijection_1004
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_1004 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> T_Σ_14
d_bijective_1016 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0))
-- Function.Bundles._.Bijection.injection
d_injection_1022 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> T_Injection_842
d_injection_1022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Injection_842
d_injection_1022 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Bijection_1004
v6 = T_Bijection_1004 -> T_Injection_842
du_injection_1022 T_Bijection_1004
v6
du_injection_1022 :: T_Bijection_1004 -> T_Injection_842
du_injection_1022 :: T_Bijection_1004 -> T_Injection_842
du_injection_1022 T_Bijection_1004
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Injection_842)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Injection_842
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Injection_842
C_constructor_916 ((T_Bijection_1004 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> AgdaAny -> AgdaAny
d_to_1012 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0))
      ((T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1014 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0)) ((T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_1018 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0))
-- Function.Bundles._.Bijection.surjection
d_surjection_1024 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> T_Surjection_918
d_surjection_1024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Surjection_918
d_surjection_1024 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Bijection_1004 -> T_Surjection_918
du_surjection_1024 T_Bijection_1004
v6
du_surjection_1024 :: T_Bijection_1004 -> T_Surjection_918
du_surjection_1024 :: T_Bijection_1004 -> T_Surjection_918
du_surjection_1024 T_Bijection_1004
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_918)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_918
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_918
C_constructor_1002 ((T_Bijection_1004 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> AgdaAny -> AgdaAny
d_to_1012 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0))
      ((T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1014 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0)) ((T_Bijection_1004 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> AgdaAny -> T_Σ_14
du_surjective_1020 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0))
-- Function.Bundles._.Bijection._.isInjection
d_isInjection_1028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_98
d_isInjection_1028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_IsInjection_98
d_isInjection_1028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsInjection_98
du_isInjection_1028 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_isInjection_1028 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_98
du_isInjection_1028 :: T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsInjection_98
du_isInjection_1028 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = (T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsInjection_98)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsInjection_98
forall a b. a -> b
coe
      T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsInjection_98
du_isInjection_914 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
      ((T_Bijection_1004 -> T_Injection_842) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> T_Injection_842
du_injection_1022 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2))
-- Function.Bundles._.Bijection._.isSurjection
d_isSurjection_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
d_isSurjection_1032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_IsSurjection_174
d_isSurjection_1032 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsSurjection_174
du_isSurjection_1032 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_isSurjection_1032 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
du_isSurjection_1032 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsSurjection_174
du_isSurjection_1032 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = (T_Setoid_46
 -> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174
du_isSurjection_990 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
      ((T_Bijection_1004 -> T_Surjection_918) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> T_Surjection_918
du_surjection_1024 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2))
-- Function.Bundles._.Bijection._.strictlySurjective
d_strictlySurjective_1034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_1034 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_1034 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> AgdaAny -> T_Σ_14
du_strictlySurjective_1034 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_strictlySurjective_1034 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_1034 :: T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> AgdaAny -> T_Σ_14
du_strictlySurjective_1034 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Bijection_1004 -> T_Surjection_918) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> T_Surjection_918
du_surjection_1024 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsSurjection_174 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSurjection_174 -> AgdaAny -> T_Σ_14
MAlonzo.Code.Function.Structures.du_strictlySurjective_246
         ((T_Setoid_46
 -> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_Surjection_918 -> T_IsSurjection_174
du_isSurjection_990 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Bijection._.to⁻
d_to'8315'_1036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny
d_to'8315'_1036 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
d_to'8315'_1036 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Bijection_1004
v6 = T_Bijection_1004 -> AgdaAny -> AgdaAny
du_to'8315'_1036 T_Bijection_1004
v6
du_to'8315'_1036 :: T_Bijection_1004 -> AgdaAny -> AgdaAny
du_to'8315'_1036 :: T_Bijection_1004 -> AgdaAny -> AgdaAny
du_to'8315'_1036 T_Bijection_1004
v0
  = (T_Surjection_918 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_918 -> AgdaAny -> AgdaAny
du_to'8315'_996 ((T_Bijection_1004 -> T_Surjection_918) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> T_Surjection_918
du_surjection_1024 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v0))
-- Function.Bundles._.Bijection.isBijection
d_isBijection_1038 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256
d_isBijection_1038 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_IsBijection_256
d_isBijection_1038 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_isBijection_1038 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Function.Structures.T_IsBijection_256
du_isBijection_1038 :: T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = (T_IsInjection_98 -> (AgdaAny -> T_Σ_14) -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe
      T_IsInjection_98 -> (AgdaAny -> T_Σ_14) -> T_IsBijection_256
MAlonzo.Code.Function.Structures.C_constructor_340
      ((T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsInjection_98)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_Setoid_46 -> T_Injection_842 -> T_IsInjection_98
du_isInjection_914 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
         ((T_Bijection_1004 -> T_Injection_842) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> T_Injection_842
du_injection_1022 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2)))
      ((T_Bijection_1004 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004 -> AgdaAny -> T_Σ_14
du_surjective_1020 (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2))
-- Function.Bundles._.Bijection._.Eq₁._≈_
d__'8776'__1044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1044 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1044 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁._≉_
d__'8777'__1046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1046 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1046 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁.Carrier
d_Carrier_1048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> ()
d_Carrier_1048 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Level_18
d_Carrier_1048 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁.isEquivalence
d_isEquivalence_1050 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1050 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_IsEquivalence_28
d_isEquivalence_1050 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsEquivalence_28
du_isEquivalence_1050 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_isEquivalence_1050 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1050 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsEquivalence_28
du_isEquivalence_1050 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_1052 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1052 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1052 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1052 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_isPartialEquivalence_1052 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1052 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1052 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Bijection._.Eq₁.partialSetoid
d_partialSetoid_1054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1054 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_PartialSetoid_10
d_partialSetoid_1054 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_PartialSetoid_10
du_partialSetoid_1054 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_partialSetoid_1054 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1054 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_PartialSetoid_10
du_partialSetoid_1054 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
               ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_1056 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1056 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_RawSetoid_12
d_rawSetoid_1056 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁.refl
d_refl_1058 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny
d_refl_1058 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
d_refl_1058 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> AgdaAny -> AgdaAny
du_refl_1058 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_refl_1058 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny
du_refl_1058 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> AgdaAny -> AgdaAny
du_refl_1058 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
               ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_28
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_1060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1060 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1060 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1060 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_reflexive_1060 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1060 :: T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1060 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Bijection._.Eq₁.setoid
d_setoid_1062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1062 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Setoid_46
d_setoid_1062 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_Setoid_46
du_setoid_1062 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_setoid_1062 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1062 :: T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_Setoid_46
du_setoid_1062 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
            ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v4))))
-- Function.Bundles._.Bijection._.Eq₁.sym
d_sym_1064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1064 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1064 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_sym_1064 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1064 :: T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1064 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Bijection._.Eq₁.trans
d_trans_1066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1066 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1066 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1066 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_trans_1066 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1066 :: T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1066 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Bijection._.Eq₂._≈_
d__'8776'__1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1070 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂._≉_
d__'8777'__1072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1072 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂.Carrier
d_Carrier_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> ()
d_Carrier_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Level_18
d_Carrier_1074 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂.isEquivalence
d_isEquivalence_1076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1076 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_IsEquivalence_28
d_isEquivalence_1076 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsEquivalence_28
du_isEquivalence_1076 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_isEquivalence_1076 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1076 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsEquivalence_28
du_isEquivalence_1076 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1078 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1078 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_isPartialEquivalence_1078 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1078 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1078 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Bijection._.Eq₂.partialSetoid
d_partialSetoid_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_PartialSetoid_10
d_partialSetoid_1080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_PartialSetoid_10
du_partialSetoid_1080 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_partialSetoid_1080 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1080 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> T_PartialSetoid_10
du_partialSetoid_1080 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
               ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₂.rawSetoid
d_rawSetoid_1082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_RawSetoid_12
d_rawSetoid_1082 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂.refl
d_refl_1084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny
d_refl_1084 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
d_refl_1084 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> AgdaAny -> AgdaAny
du_refl_1084 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_refl_1084 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny
du_refl_1084 :: T_Setoid_46
-> T_Setoid_46 -> T_Bijection_1004 -> AgdaAny -> AgdaAny
du_refl_1084 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
               ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_28
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_1086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1086 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1086 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1086 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_reflexive_1086 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1086 :: T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1086 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Bijection._.Eq₂.setoid
d_setoid_1088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> T_Setoid_46
d_setoid_1088 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_Setoid_46
du_setoid_1088 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_setoid_1088 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1088 :: T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_Setoid_46
du_setoid_1088 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
            ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v4))))
-- Function.Bundles._.Bijection._.Eq₂.sym
d_sym_1090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1090 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1090 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1090 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_sym_1090 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1090 :: T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1090 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Bijection._.Eq₂.trans
d_trans_1092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1092 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1092 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1092 T_Setoid_46
v4 T_Setoid_46
v5 T_Bijection_1004
v6
du_trans_1092 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Bijection_1004 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1092 :: T_Setoid_46
-> T_Setoid_46
-> T_Bijection_1004
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1092 T_Setoid_46
v0 T_Setoid_46
v1 T_Bijection_1004
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Bijection_1004 -> T_IsBijection_256
du_isBijection_1038 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Bijection_1004 -> AgdaAny
forall a b. a -> b
coe T_Bijection_1004
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_98
v4
             = T_IsBijection_256 -> T_IsInjection_98
MAlonzo.Code.Function.Structures.d_isInjection_264 (AgdaAny -> T_IsBijection_256
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_98 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._._._≈_
d__'8776'__1114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1114 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Carrier
d_Carrier_1116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 -> ()
d_Carrier_1116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
d_Carrier_1116 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBiInverse
d_IsBiInverse_1130 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBiInverse_1130 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
-- Function.Bundles._._.IsCongruent
d_IsCongruent_1138 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCongruent_1138 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsInverse
d_IsInverse_1146 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInverse_1146 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsLeftInverse
d_IsLeftInverse_1150 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLeftInverse_1150 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsRightInverse
d_IsRightInverse_1154 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRightInverse_1154 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsSplitSurjection
d_IsSplitSurjection_1158 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSplitSurjection_1158 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsBiInverse.from₁-cong
d_from'8321''45'cong_1234 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_1234 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_1234 T_IsBiInverse_714
v0
  = (T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'8321''45'cong_734 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0)
-- Function.Bundles._._.IsBiInverse.from₂-cong
d_from'8322''45'cong_1236 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_1236 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_1236 T_IsBiInverse_714
v0
  = (T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'8322''45'cong_736 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0)
-- Function.Bundles._._.IsBiInverse.inverseʳ
d_inverse'691'_1238 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1238 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1238 T_IsBiInverse_714
v0
  = (T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'691'_740 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0)
-- Function.Bundles._._.IsBiInverse.inverseˡ
d_inverse'737'_1240 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1240 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1240 T_IsBiInverse_714
v0
  = (T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'737'_738 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0)
-- Function.Bundles._._.IsBiInverse.to-isCongruent
d_to'45'isCongruent_1248 ::
  MAlonzo.Code.Function.Structures.T_IsBiInverse_714 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_to'45'isCongruent_1248 :: T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_1248 T_IsBiInverse_714
v0
  = (T_IsBiInverse_714 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_IsBiInverse_714 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_to'45'isCongruent_732 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0)
-- Function.Bundles._._.IsCongruent.cong
d_cong_1378 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1378 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1378 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'_1380 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_1380 :: T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_1380 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
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'_1382 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_1382 :: T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_1382 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
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'_1506 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1506 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1506 T_IsInverse_526
v0
  = (T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'691'_538 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)
-- Function.Bundles._._.IsInverse.isLeftInverse
d_isLeftInverse_1516 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
d_isLeftInverse_1516 :: T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_1516 T_IsInverse_526
v0
  = (T_IsInverse_526 -> T_IsLeftInverse_346)
-> AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)
-- Function.Bundles._._.IsInverse.Eq₁._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1530 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1530 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁._≉_
d__'8777'__1532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1532 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1532 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁.Carrier
d_Carrier_1534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 -> ()
d_Carrier_1534 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Level_18
d_Carrier_1534 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1536 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsEquivalence_28
d_isEquivalence_1536 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_1536 T_IsInverse_526
v8
du_isEquivalence_1536 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1536 :: T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_1536 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1538 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1538 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1538 T_IsInverse_526
v8
du_isPartialEquivalence_1538 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1538 :: T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1538 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsInverse.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1540 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_PartialSetoid_10
d_partialSetoid_1540 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_1540 T_IsInverse_526
v8
du_partialSetoid_1540 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1540 :: T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_1540 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1542 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
d_rawSetoid_1542 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny
d_refl_1544 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
d_refl_1544 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8 = T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_1544 T_IsInverse_526
v8
du_refl_1544 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny
du_refl_1544 :: T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_1544 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1546 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1546 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1546 T_IsInverse_526
v8
du_reflexive_1546 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1546 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1546 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsInverse.Eq₁.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Setoid_46
d_setoid_1548 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_Setoid_46
du_setoid_1548 T_IsInverse_526
v8
du_setoid_1548 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1548 :: T_IsInverse_526 -> T_Setoid_46
du_setoid_1548 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1)))
-- Function.Bundles._._.IsInverse.Eq₁.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1550 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1550 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8 = T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1550 T_IsInverse_526
v8
du_sym_1550 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1550 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1550 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsInverse.Eq₁.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1552 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1552 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8 = T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1552 T_IsInverse_526
v8
du_trans_1552 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1552 :: T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1552 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsInverse.Eq₂._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1556 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1556 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂._≉_
d__'8777'__1558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1558 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1558 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 -> ()
d_Carrier_1560 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Level_18
d_Carrier_1560 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1562 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsEquivalence_28
d_isEquivalence_1562 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_1562 T_IsInverse_526
v8
du_isEquivalence_1562 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1562 :: T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_1562 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1564 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1564 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1564 T_IsInverse_526
v8
du_isPartialEquivalence_1564 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1564 :: T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1564 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsInverse.Eq₂.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1566 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_PartialSetoid_10
d_partialSetoid_1566 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_1566 T_IsInverse_526
v8
du_partialSetoid_1566 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1566 :: T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_1566 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₂.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1568 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
d_rawSetoid_1568 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny
d_refl_1570 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
d_refl_1570 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8 = T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_1570 T_IsInverse_526
v8
du_refl_1570 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny
du_refl_1570 :: T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_1570 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1572 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1572 T_IsInverse_526
v8
du_reflexive_1572 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1572 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1572 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsInverse.Eq₂.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Setoid_46
d_setoid_1574 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8
  = T_IsInverse_526 -> T_Setoid_46
du_setoid_1574 T_IsInverse_526
v8
du_setoid_1574 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1574 :: T_IsInverse_526 -> T_Setoid_46
du_setoid_1574 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1)))
-- Function.Bundles._._.IsInverse.Eq₂.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1576 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1576 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8 = T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1576 T_IsInverse_526
v8
du_sym_1576 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1576 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1576 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsInverse.Eq₂.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1578 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1578 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_526
v8 = T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1578 T_IsInverse_526
v8
du_trans_1578 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1578 :: T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1578 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1
          = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Bundles._._.IsLeftInverse.from-cong
d_from'45'cong_1582 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1582 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1582 T_IsLeftInverse_346
v0
  = (T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'45'cong_360 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0)
-- Function.Bundles._._.IsLeftInverse.inverseˡ
d_inverse'737'_1584 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1584 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1584 T_IsLeftInverse_346
v0
  = (T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'737'_362 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0)
-- Function.Bundles._._.IsLeftInverse.isCongruent
d_isCongruent_1586 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1586 :: T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_1586 T_IsLeftInverse_346
v0
  = (T_IsLeftInverse_346 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0)
-- Function.Bundles._._.IsLeftInverse.isSurjection
d_isSurjection_1592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
d_isSurjection_1592 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsSurjection_174
d_isSurjection_1592 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsSurjection_174
du_isSurjection_1592
du_isSurjection_1592 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
du_isSurjection_1592 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsSurjection_174
du_isSurjection_1592 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_346
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsSurjection_174
forall a b. a -> b
coe (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
MAlonzo.Code.Function.Structures.du_isSurjection_428 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_346
v2
-- Function.Bundles._._.IsLeftInverse.strictlyInverseˡ
d_strictlyInverse'737'_1594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny
d_strictlyInverse'737'_1594 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_1594 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
du_strictlyInverse'737'_1594
du_strictlyInverse'737'_1594 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny
du_strictlyInverse'737'_1594 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
du_strictlyInverse'737'_1594 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_346
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_424 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_346
v2
      AgdaAny
v3
-- Function.Bundles._._.IsLeftInverse.Eq₁._≈_
d__'8776'__1600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1600 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1600 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₁._≉_
d__'8777'__1602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1602 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1602 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₁.Carrier
d_Carrier_1604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 -> ()
d_Carrier_1604 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Level_18
d_Carrier_1604 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₁.isEquivalence
d_isEquivalence_1606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1606 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsEquivalence_28
d_isEquivalence_1606 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_1606 T_IsLeftInverse_346
v8
du_isEquivalence_1606 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1606 :: T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_1606 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
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_1608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1608 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1608 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1608 T_IsLeftInverse_346
v8
du_isPartialEquivalence_1608 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1608 :: T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1608 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsLeftInverse.Eq₁.partialSetoid
d_partialSetoid_1610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1610 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_PartialSetoid_10
d_partialSetoid_1610 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_1610 T_IsLeftInverse_346
v8
du_partialSetoid_1610 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1610 :: T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_1610 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_1612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1612 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
d_rawSetoid_1612 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₁.refl
d_refl_1614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny
d_refl_1614 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
d_refl_1614 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8 = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_1614 T_IsLeftInverse_346
v8
du_refl_1614 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny
du_refl_1614 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_1614 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_1616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1616 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1616 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1616 T_IsLeftInverse_346
v8
du_reflexive_1616 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1616 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1616 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Bundles._._.IsLeftInverse.Eq₁.setoid
d_setoid_1618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1618 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Setoid_46
d_setoid_1618 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_1618 T_IsLeftInverse_346
v8
du_setoid_1618 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1618 :: T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_1618 T_IsLeftInverse_346
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0))
-- Function.Bundles._._.IsLeftInverse.Eq₁.sym
d_sym_1620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1620 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1620 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8 = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1620 T_IsLeftInverse_346
v8
du_sym_1620 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1620 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1620 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsLeftInverse.Eq₁.trans
d_trans_1622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1622 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1622 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8 = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1622 T_IsLeftInverse_346
v8
du_trans_1622 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1622 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1622 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsLeftInverse.Eq₂._≈_
d__'8776'__1626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1626 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1626 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₂._≉_
d__'8777'__1628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1628 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1628 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₂.Carrier
d_Carrier_1630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 -> ()
d_Carrier_1630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Level_18
d_Carrier_1630 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₂.isEquivalence
d_isEquivalence_1632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsEquivalence_28
d_isEquivalence_1632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_1632 T_IsLeftInverse_346
v8
du_isEquivalence_1632 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1632 :: T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_1632 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
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_1634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1634 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1634 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1634 T_IsLeftInverse_346
v8
du_isPartialEquivalence_1634 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1634 :: T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1634 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsLeftInverse.Eq₂.partialSetoid
d_partialSetoid_1636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1636 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_PartialSetoid_10
d_partialSetoid_1636 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_1636 T_IsLeftInverse_346
v8
du_partialSetoid_1636 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1636 :: T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_1636 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsLeftInverse.Eq₂.rawSetoid
d_rawSetoid_1638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1638 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
d_rawSetoid_1638 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsLeftInverse.Eq₂.refl
d_refl_1640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny
d_refl_1640 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
d_refl_1640 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8 = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_1640 T_IsLeftInverse_346
v8
du_refl_1640 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny
du_refl_1640 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_1640 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_1642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1642 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1642 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1642 T_IsLeftInverse_346
v8
du_reflexive_1642 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1642 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1642 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Bundles._._.IsLeftInverse.Eq₂.setoid
d_setoid_1644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1644 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Setoid_46
d_setoid_1644 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8
  = T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_1644 T_IsLeftInverse_346
v8
du_setoid_1644 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1644 :: T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_1644 T_IsLeftInverse_346
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
      ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0))
-- Function.Bundles._._.IsLeftInverse.Eq₂.sym
d_sym_1646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1646 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1646 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8 = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1646 T_IsLeftInverse_346
v8
du_sym_1646 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1646 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1646 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsLeftInverse.Eq₂.trans
d_trans_1648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1648 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1648 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsLeftInverse_346
v8 = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1648 T_IsLeftInverse_346
v8
du_trans_1648 ::
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1648 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1648 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsRightInverse.from-cong
d_from'45'cong_1652 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1652 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1652 T_IsRightInverse_438
v0
  = (T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from'45'cong_452 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0)
-- Function.Bundles._._.IsRightInverse.inverseʳ
d_inverse'691'_1654 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1654 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_1654 T_IsRightInverse_438
v0
  = (T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_inverse'691'_454 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0)
-- Function.Bundles._._.IsRightInverse.isCongruent
d_isCongruent_1656 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1656 :: T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_1656 T_IsRightInverse_438
v0
  = (T_IsRightInverse_438 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0)
-- Function.Bundles._._.IsRightInverse.strictlyInverseʳ
d_strictlyInverse'691'_1662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny
d_strictlyInverse'691'_1662 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_1662 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
du_strictlyInverse'691'_1662
du_strictlyInverse'691'_1662 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny
du_strictlyInverse'691'_1662 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
du_strictlyInverse'691'_1662 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_IsRightInverse_438
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'691'_516 AgdaAny -> AgdaAny
v0 T_IsRightInverse_438
v2
      AgdaAny
v3
-- Function.Bundles._._.IsRightInverse.Eq₁._≈_
d__'8776'__1668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1668 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1668 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₁._≉_
d__'8777'__1670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1670 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1670 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₁.Carrier
d_Carrier_1672 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 -> ()
d_Carrier_1672 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Level_18
d_Carrier_1672 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₁.isEquivalence
d_isEquivalence_1674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1674 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsEquivalence_28
d_isEquivalence_1674 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_1674 T_IsRightInverse_438
v8
du_isEquivalence_1674 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1674 :: T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_1674 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
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_1676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1676 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1676 T_IsRightInverse_438
v8
du_isPartialEquivalence_1676 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1676 :: T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1676 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsRightInverse.Eq₁.partialSetoid
d_partialSetoid_1678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_PartialSetoid_10
d_partialSetoid_1678 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_1678 T_IsRightInverse_438
v8
du_partialSetoid_1678 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1678 :: T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_1678 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_1680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
d_rawSetoid_1680 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₁.refl
d_refl_1682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny
d_refl_1682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
d_refl_1682 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8 = T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_1682 T_IsRightInverse_438
v8
du_refl_1682 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny
du_refl_1682 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_1682 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_1684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1684 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1684 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1684 T_IsRightInverse_438
v8
du_reflexive_1684 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1684 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1684 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Bundles._._.IsRightInverse.Eq₁.setoid
d_setoid_1686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Setoid_46
d_setoid_1686 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_Setoid_46
du_setoid_1686 T_IsRightInverse_438
v8
du_setoid_1686 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1686 :: T_IsRightInverse_438 -> T_Setoid_46
du_setoid_1686 T_IsRightInverse_438
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0))
-- Function.Bundles._._.IsRightInverse.Eq₁.sym
d_sym_1688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1688 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1688 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8 = T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1688 T_IsRightInverse_438
v8
du_sym_1688 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1688 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1688 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsRightInverse.Eq₁.trans
d_trans_1690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1690 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1690 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8 = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1690 T_IsRightInverse_438
v8
du_trans_1690 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1690 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1690 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsRightInverse.Eq₂._≈_
d__'8776'__1694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1694 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1694 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₂._≉_
d__'8777'__1696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__1696 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1696 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₂.Carrier
d_Carrier_1698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 -> ()
d_Carrier_1698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Level_18
d_Carrier_1698 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₂.isEquivalence
d_isEquivalence_1700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1700 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsEquivalence_28
d_isEquivalence_1700 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_1700 T_IsRightInverse_438
v8
du_isEquivalence_1700 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1700 :: T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_1700 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_28
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_1702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1702 T_IsRightInverse_438
v8
du_isPartialEquivalence_1702 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1702 :: T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1702 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsRightInverse.Eq₂.partialSetoid
d_partialSetoid_1704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_PartialSetoid_10
d_partialSetoid_1704 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_1704 T_IsRightInverse_438
v8
du_partialSetoid_1704 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1704 :: T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_1704 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Bundles._._.IsRightInverse.Eq₂.rawSetoid
d_rawSetoid_1706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1706 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
d_rawSetoid_1706 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._._.IsRightInverse.Eq₂.refl
d_refl_1708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny
d_refl_1708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
d_refl_1708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8 = T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_1708 T_IsRightInverse_438
v8
du_refl_1708 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny
du_refl_1708 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_1708 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_1710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1710 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1710 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1710 T_IsRightInverse_438
v8
du_reflexive_1710 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1710 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1710 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Bundles._._.IsRightInverse.Eq₂.setoid
d_setoid_1712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Setoid_46
d_setoid_1712 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8
  = T_IsRightInverse_438 -> T_Setoid_46
du_setoid_1712 T_IsRightInverse_438
v8
du_setoid_1712 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1712 :: T_IsRightInverse_438 -> T_Setoid_46
du_setoid_1712 T_IsRightInverse_438
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
      ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0))
-- Function.Bundles._._.IsRightInverse.Eq₂.sym
d_sym_1714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1714 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1714 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8 = T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1714 T_IsRightInverse_438
v8
du_sym_1714 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1714 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1714 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsRightInverse.Eq₂.trans
d_trans_1716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1716 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1716 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsRightInverse_438
v8 = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1716 T_IsRightInverse_438
v8
du_trans_1716 ::
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1716 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1716 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1
          = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Bundles._._.IsSplitSurjection.from
d_from_1720 ::
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_806 ->
  AgdaAny -> AgdaAny
d_from_1720 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_from_1720 T_IsSplitSurjection_806
v0
  = (T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.d_from_814 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0)
-- Function.Bundles._._.IsSplitSurjection.isLeftInverse
d_isLeftInverse_1732 ::
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_806 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
d_isLeftInverse_1732 :: T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_1732 T_IsSplitSurjection_806
v0
  = (T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0)
-- Function.Bundles._.Equivalence
d_Equivalence_1858 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Equivalence_1858 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Equivalence_1858
  = C_constructor_1940 (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Equivalence.to
d_to_1868 :: T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_to_1868 :: T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_to_1868 T_Equivalence_1858
v0
  = case T_Equivalence_1858 -> T_Equivalence_1858
forall a b. a -> b
coe T_Equivalence_1858
v0 of
      C_constructor_1940 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_1858
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.from
d_from_1870 :: T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_from_1870 :: T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_from_1870 T_Equivalence_1858
v0
  = case T_Equivalence_1858 -> T_Equivalence_1858
forall a b. a -> b
coe T_Equivalence_1858
v0 of
      C_constructor_1940 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_1858
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.to-cong
d_to'45'cong_1872 ::
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1872 :: T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1872 T_Equivalence_1858
v0
  = case T_Equivalence_1858 -> T_Equivalence_1858
forall a b. a -> b
coe T_Equivalence_1858
v0 of
      C_constructor_1940 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_1858
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.from-cong
d_from'45'cong_1874 ::
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1874 :: T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1874 T_Equivalence_1858
v0
  = case T_Equivalence_1858 -> T_Equivalence_1858
forall a b. a -> b
coe T_Equivalence_1858
v0 of
      C_constructor_1940 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_1858
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.toFunction
d_toFunction_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> T_Func_774
d_toFunction_1876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Func_774
d_toFunction_1876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 T_Equivalence_1858
v6
du_toFunction_1876 :: T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 :: T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 T_Equivalence_1858
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774)
-> AgdaAny -> AgdaAny -> T_Func_774
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774
C_constructor_840 ((T_Equivalence_1858 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_to_1868 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v0))
      ((T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1872 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v0))
-- Function.Bundles._.Equivalence._.isCongruent
d_isCongruent_1880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_IsCongruent_22
d_isCongruent_1880 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsCongruent_22
du_isCongruent_1880 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_isCongruent_1880 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1880 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsCongruent_22
du_isCongruent_1880 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
      ((T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2))
-- Function.Bundles._.Equivalence._.Eq₁._≈_
d__'8776'__1884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1884 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₁._≉_
d__'8777'__1886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1886 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₁.Carrier
d_Carrier_1888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> ()
d_Carrier_1888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Level_18
d_Carrier_1888 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₁.isEquivalence
d_isEquivalence_1890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1890 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_IsEquivalence_28
d_isEquivalence_1890 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsEquivalence_28
du_isEquivalence_1890 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_isEquivalence_1890 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1890 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsEquivalence_28
du_isEquivalence_1890 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
-- Function.Bundles._.Equivalence._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1892 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1892 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_isPartialEquivalence_1892 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1892 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1892 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Equivalence._.Eq₁.partialSetoid
d_partialSetoid_1894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_PartialSetoid_10
d_partialSetoid_1894 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_PartialSetoid_10
du_partialSetoid_1894 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_partialSetoid_1894 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1894 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_PartialSetoid_10
du_partialSetoid_1894 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Equivalence._.Eq₁.rawSetoid
d_rawSetoid_1896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_RawSetoid_12
d_rawSetoid_1896 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₁.refl
d_refl_1898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_refl_1898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
d_refl_1898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> AgdaAny -> AgdaAny
du_refl_1898 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_refl_1898 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny
du_refl_1898 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> AgdaAny -> AgdaAny
du_refl_1898 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Equivalence._.Eq₁.reflexive
d_reflexive_1900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1900 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1900 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_reflexive_1900 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1900 :: T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1900 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Equivalence._.Eq₁.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Setoid_46
d_setoid_1902 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Equivalence_1858 -> T_Setoid_46
du_setoid_1902 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_setoid_1902 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1902 :: T_Setoid_46 -> T_Setoid_46 -> T_Equivalence_1858 -> T_Setoid_46
du_setoid_1902 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Equivalence._.Eq₁.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1904 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1904 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_sym_1904 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1904 :: T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1904 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Equivalence._.Eq₁.trans
d_trans_1906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1906 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1906 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_trans_1906 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1906 :: T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1906 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Equivalence._.Eq₂._≈_
d__'8776'__1910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1910 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₂._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1912 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₂.Carrier
d_Carrier_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> ()
d_Carrier_1914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Level_18
d_Carrier_1914 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₂.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1916 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_IsEquivalence_28
d_isEquivalence_1916 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsEquivalence_28
du_isEquivalence_1916 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_isEquivalence_1916 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1916 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsEquivalence_28
du_isEquivalence_1916 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
-- Function.Bundles._.Equivalence._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1918 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_isPartialEquivalence_1918 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1918 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1918 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Equivalence._.Eq₂.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_PartialSetoid_10
d_partialSetoid_1920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_PartialSetoid_10
du_partialSetoid_1920 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_partialSetoid_1920 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1920 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_PartialSetoid_10
du_partialSetoid_1920 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Equivalence._.Eq₂.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_RawSetoid_12
d_rawSetoid_1922 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Equivalence._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_refl_1924 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
d_refl_1924 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> AgdaAny -> AgdaAny
du_refl_1924 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_refl_1924 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny
du_refl_1924 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> AgdaAny -> AgdaAny
du_refl_1924 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Function.Bundles._.Equivalence._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  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_46
-> T_Setoid_46
-> T_Equivalence_1858
-> 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_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1926 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_reflexive_1926 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1926 :: T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1926 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Equivalence._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1928 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Setoid_46
d_setoid_1928 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Equivalence_1858 -> T_Setoid_46
du_setoid_1928 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_setoid_1928 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1928 :: T_Setoid_46 -> T_Setoid_46 -> T_Equivalence_1858 -> T_Setoid_46
du_setoid_1928 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Equivalence._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1930 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> 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_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1930 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_sym_1930 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1930 :: T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1930 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Equivalence._.Eq₂.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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1932 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> 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_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1932 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_trans_1932 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1932 :: T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1932 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = let v3 :: AgdaAny
v3 = (T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_toFunction_1876 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: AgdaAny
v4 = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.Equivalence.fromFunction
d_fromFunction_1934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 -> T_Func_774
d_fromFunction_1934 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_Func_774
d_fromFunction_1934 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Equivalence_1858 -> T_Func_774
du_fromFunction_1934 T_Equivalence_1858
v6
du_fromFunction_1934 :: T_Equivalence_1858 -> T_Func_774
du_fromFunction_1934 :: T_Equivalence_1858 -> T_Func_774
du_fromFunction_1934 T_Equivalence_1858
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774)
-> AgdaAny -> AgdaAny -> T_Func_774
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774
C_constructor_840 ((T_Equivalence_1858 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> AgdaAny -> AgdaAny
d_from_1870 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v0))
      ((T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1874 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v0))
-- Function.Bundles._.Equivalence._.isCongruent
d_isCongruent_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1938 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Equivalence_1858
-> T_IsCongruent_22
d_isCongruent_1938 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsCongruent_22
du_isCongruent_1938 T_Setoid_46
v4 T_Setoid_46
v5 T_Equivalence_1858
v6
du_isCongruent_1938 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Equivalence_1858 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1938 :: T_Setoid_46
-> T_Setoid_46 -> T_Equivalence_1858 -> T_IsCongruent_22
du_isCongruent_1938 T_Setoid_46
v0 T_Setoid_46
v1 T_Equivalence_1858
v2
  = (T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_46 -> T_Setoid_46 -> T_Func_774 -> T_IsCongruent_22
du_isCongruent_784 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0)
      ((T_Equivalence_1858 -> T_Func_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858 -> T_Func_774
du_fromFunction_1934 (T_Equivalence_1858 -> AgdaAny
forall a b. a -> b
coe T_Equivalence_1858
v2))
-- Function.Bundles._.LeftInverse
d_LeftInverse_1942 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_LeftInverse_1942 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_LeftInverse_1942
  = C_constructor_2034 (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.LeftInverse.to
d_to_1954 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_to_1954 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_to_1954 T_LeftInverse_1942
v0
  = case T_LeftInverse_1942 -> T_LeftInverse_1942
forall a b. a -> b
coe T_LeftInverse_1942
v0 of
      C_constructor_2034 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_1942
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.from
d_from_1956 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 T_LeftInverse_1942
v0
  = case T_LeftInverse_1942 -> T_LeftInverse_1942
forall a b. a -> b
coe T_LeftInverse_1942
v0 of
      C_constructor_2034 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_1942
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.to-cong
d_to'45'cong_1958 ::
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1958 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1958 T_LeftInverse_1942
v0
  = case T_LeftInverse_1942 -> T_LeftInverse_1942
forall a b. a -> b
coe T_LeftInverse_1942
v0 of
      C_constructor_2034 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_1942
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.from-cong
d_from'45'cong_1960 ::
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1960 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1960 T_LeftInverse_1942
v0
  = case T_LeftInverse_1942 -> T_LeftInverse_1942
forall a b. a -> b
coe T_LeftInverse_1942
v0 of
      C_constructor_2034 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_1942
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.inverseˡ
d_inverse'737'_1962 ::
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1962 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1962 T_LeftInverse_1942
v0
  = case T_LeftInverse_1942 -> T_LeftInverse_1942
forall a b. a -> b
coe T_LeftInverse_1942
v0 of
      C_constructor_2034 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_1942
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.isCongruent
d_isCongruent_1964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsCongruent_22
d_isCongruent_1964 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22
du_isCongruent_1964 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isCongruent_1964 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1964 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22
du_isCongruent_1964 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_constructor_94
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1958 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1))
-- Function.Bundles._.LeftInverse.isLeftInverse
d_isLeftInverse_1966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
d_isLeftInverse_1966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsLeftInverse_346
d_isLeftInverse_1966 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isLeftInverse_1966 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
du_isLeftInverse_1966 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.C_constructor_432
      ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22
du_isCongruent_1964 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1960 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1962 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
-- Function.Bundles._.LeftInverse._.isSurjection
d_isSurjection_1970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
d_isSurjection_1970 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsSurjection_174
d_isSurjection_1970 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSurjection_174
du_isSurjection_1970 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isSurjection_1970 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
du_isSurjection_1970 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSurjection_174
du_isSurjection_1970 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
MAlonzo.Code.Function.Structures.du_isSurjection_428
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
-- Function.Bundles._.LeftInverse._.strictlyInverseˡ
d_strictlyInverse'737'_1972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_1972 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_1972 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1972 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_strictlyInverse'737'_1972 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1972 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_1972 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_424
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
-- Function.Bundles._.LeftInverse._.Eq₁._≈_
d__'8776'__1976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1976 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁._≉_
d__'8777'__1978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1978 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁.Carrier
d_Carrier_1980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> ()
d_Carrier_1980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
d_Carrier_1980 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsEquivalence_28
d_isEquivalence_1982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_1982 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isEquivalence_1982 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_1982 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_1982 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1984 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isPartialEquivalence_1984 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1984 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1984 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_PartialSetoid_10
d_partialSetoid_1986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_1986 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_partialSetoid_1986 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1986 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_1986 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_1988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
d_rawSetoid_1988 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁.refl
d_refl_1990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_refl_1990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
d_refl_1990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_1990 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_refl_1990 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_1990 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_1990 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1992 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1992 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_reflexive_1992 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1992 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1992 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.LeftInverse._.Eq₁.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Setoid_46
d_setoid_1994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_1994 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_setoid_1994 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1994 :: T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_1994 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.LeftInverse._.Eq₁.sym
d_sym_1996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1996 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_sym_1996 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1996 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1996 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₁.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1998 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_trans_1998 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1998 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1998 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₂._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2002 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂._≉_
d__'8777'__2004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2004 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂.Carrier
d_Carrier_2006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> ()
d_Carrier_2006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
d_Carrier_2006 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsEquivalence_28
d_isEquivalence_2008 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_2008 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isEquivalence_2008 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2008 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_2008 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2010 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isPartialEquivalence_2010 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2010 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2010 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₂.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_PartialSetoid_10
d_partialSetoid_2012 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_2012 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_partialSetoid_2012 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2012 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_2012 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.LeftInverse._.Eq₂.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_2014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
d_rawSetoid_2014 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_refl_2016 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
d_refl_2016 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2016 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_refl_2016 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2016 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2016 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2018 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2018 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2018 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_reflexive_2018 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2018 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2018 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.LeftInverse._.Eq₂.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Setoid_46
d_setoid_2020 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_2020 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_setoid_2020 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2020 :: T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_2020 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.LeftInverse._.Eq₂.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2022 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2022 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_sym_2022 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2022 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2022 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.LeftInverse._.Eq₂.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2024 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2024 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_trans_2024 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2024 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2024 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.LeftInverse.equivalence
d_equivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> T_Equivalence_1858
d_equivalence_2026 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Equivalence_1858
d_equivalence_2026 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_LeftInverse_1942 -> T_Equivalence_1858
du_equivalence_2026 T_LeftInverse_1942
v6
du_equivalence_2026 :: T_LeftInverse_1942 -> T_Equivalence_1858
du_equivalence_2026 :: T_LeftInverse_1942 -> T_Equivalence_1858
du_equivalence_2026 T_LeftInverse_1942
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_1858)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_1858
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_1858
C_constructor_1940 ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_to_1954 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0))
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)) ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1958 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0))
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1960 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0))
-- Function.Bundles._.LeftInverse.isSplitSurjection
d_isSplitSurjection_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_806
d_isSplitSurjection_2028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsSplitSurjection_806
d_isSplitSurjection_2028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSplitSurjection_806
du_isSplitSurjection_2028 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isSplitSurjection_2028 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_806
du_isSplitSurjection_2028 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSplitSurjection_806
du_isSplitSurjection_2028 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = ((AgdaAny -> AgdaAny)
 -> T_IsLeftInverse_346 -> T_IsSplitSurjection_806)
-> AgdaAny -> AgdaAny -> T_IsSplitSurjection_806
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346 -> T_IsSplitSurjection_806
MAlonzo.Code.Function.Structures.C_constructor_888
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
-- Function.Bundles._.LeftInverse.surjection
d_surjection_2030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> T_Surjection_918
d_surjection_2030 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Surjection_918
d_surjection_2030 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_LeftInverse_1942 -> T_Surjection_918
du_surjection_2030 T_LeftInverse_1942
v6
du_surjection_2030 :: T_LeftInverse_1942 -> T_Surjection_918
du_surjection_2030 :: T_LeftInverse_1942 -> T_Surjection_918
du_surjection_2030 T_LeftInverse_1942
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_918)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_918
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_918
C_constructor_1002 ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_to_1954 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0))
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1958 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
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_1942 -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 T_LeftInverse_1942
v0 AgdaAny
v1)
              ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1962 T_LeftInverse_1942
v0 AgdaAny
v1)))
-- Function.Bundles._.RightInverse
d_RightInverse_2036 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_RightInverse_2036 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_RightInverse_2036
  = C_constructor_2120 (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.RightInverse.to
d_to_2048 :: T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_to_2048 :: T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_to_2048 T_RightInverse_2036
v0
  = case T_RightInverse_2036 -> T_RightInverse_2036
forall a b. a -> b
coe T_RightInverse_2036
v0 of
      C_constructor_2120 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_2036
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.from
d_from_2050 :: T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_from_2050 :: T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_from_2050 T_RightInverse_2036
v0
  = case T_RightInverse_2036 -> T_RightInverse_2036
forall a b. a -> b
coe T_RightInverse_2036
v0 of
      C_constructor_2120 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_2036
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.to-cong
d_to'45'cong_2052 ::
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2052 :: T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2052 T_RightInverse_2036
v0
  = case T_RightInverse_2036 -> T_RightInverse_2036
forall a b. a -> b
coe T_RightInverse_2036
v0 of
      C_constructor_2120 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_2036
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.from-cong
d_from'45'cong_2054 ::
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2054 :: T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2054 T_RightInverse_2036
v0
  = case T_RightInverse_2036 -> T_RightInverse_2036
forall a b. a -> b
coe T_RightInverse_2036
v0 of
      C_constructor_2120 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_2036
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.inverseʳ
d_inverse'691'_2056 ::
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2056 :: T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2056 T_RightInverse_2036
v0
  = case T_RightInverse_2036 -> T_RightInverse_2036
forall a b. a -> b
coe T_RightInverse_2036
v0 of
      C_constructor_2120 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_2036
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.isCongruent
d_isCongruent_2058 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_2058 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_IsCongruent_22
d_isCongruent_2058 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsCongruent_22
du_isCongruent_2058 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_isCongruent_2058 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_2058 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsCongruent_22
du_isCongruent_2058 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_constructor_94
      ((T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2052 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1))
-- Function.Bundles._.RightInverse.isRightInverse
d_isRightInverse_2060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438
d_isRightInverse_2060 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_IsRightInverse_438
d_isRightInverse_2060 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_isRightInverse_2060 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438
du_isRightInverse_2060 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
MAlonzo.Code.Function.Structures.C_constructor_520
      ((T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsCongruent_22
du_isCongruent_2058 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2))
      ((T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2054 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2))
      ((T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2056 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2))
-- Function.Bundles._.RightInverse._.strictlyInverseʳ
d_strictlyInverse'691'_2064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_2064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_2064 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2064 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_strictlyInverse'691'_2064 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2064 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2064 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = ((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'691'_516
      ((T_RightInverse_2036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_to_2048 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2))
      ((T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2))
-- Function.Bundles._.RightInverse._.Eq₁._≈_
d__'8776'__2068 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2068 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2068 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₁._≉_
d__'8777'__2070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2070 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₁.Carrier
d_Carrier_2072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> ()
d_Carrier_2072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_Level_18
d_Carrier_2072 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₁.isEquivalence
d_isEquivalence_2074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_IsEquivalence_28
d_isEquivalence_2074 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsEquivalence_28
du_isEquivalence_2074 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_isEquivalence_2074 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2074 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsEquivalence_28
du_isEquivalence_2074 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_2076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2076 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2076 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2076 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_isPartialEquivalence_2076 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2076 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2076 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.RightInverse._.Eq₁.partialSetoid
d_partialSetoid_2078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_PartialSetoid_10
d_partialSetoid_2078 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_PartialSetoid_10
du_partialSetoid_2078 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_partialSetoid_2078 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2078 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_PartialSetoid_10
du_partialSetoid_2078 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_2080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_2080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_RawSetoid_12
d_rawSetoid_2080 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₁.refl
d_refl_2082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_refl_2082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
d_refl_2082 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_refl_2082 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_refl_2082 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_refl_2082 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_refl_2082 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_2084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2084 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2084 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2084 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_reflexive_2084 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2084 :: T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2084 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.RightInverse._.Eq₁.setoid
d_setoid_2086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2086 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_Setoid_46
d_setoid_2086 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46 -> T_Setoid_46 -> T_RightInverse_2036 -> T_Setoid_46
du_setoid_2086 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_setoid_2086 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2086 :: T_Setoid_46 -> T_Setoid_46 -> T_RightInverse_2036 -> T_Setoid_46
du_setoid_2086 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.RightInverse._.Eq₁.sym
d_sym_2088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2088 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2088 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_sym_2088 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2088 :: T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2088 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.RightInverse._.Eq₁.trans
d_trans_2090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2090 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2090 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2090 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_trans_2090 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2090 :: T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2090 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.RightInverse._.Eq₂._≈_
d__'8776'__2094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2094 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2094 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₂._≉_
d__'8777'__2096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2096 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2096 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₂.Carrier
d_Carrier_2098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> ()
d_Carrier_2098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_Level_18
d_Carrier_2098 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₂.isEquivalence
d_isEquivalence_2100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_IsEquivalence_28
d_isEquivalence_2100 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsEquivalence_28
du_isEquivalence_2100 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_isEquivalence_2100 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2100 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsEquivalence_28
du_isEquivalence_2100 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_2102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2102 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2102 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2102 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_isPartialEquivalence_2102 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2102 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2102 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.RightInverse._.Eq₂.partialSetoid
d_partialSetoid_2104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_PartialSetoid_10
d_partialSetoid_2104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_PartialSetoid_10
du_partialSetoid_2104 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_partialSetoid_2104 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2104 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_PartialSetoid_10
du_partialSetoid_2104 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.RightInverse._.Eq₂.rawSetoid
d_rawSetoid_2106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_2106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_RawSetoid_12
d_rawSetoid_2106 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.RightInverse._.Eq₂.refl
d_refl_2108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_refl_2108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
d_refl_2108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_refl_2108 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_refl_2108 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_refl_2108 :: T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> AgdaAny -> AgdaAny
du_refl_2108 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_2110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2110 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2110 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2110 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_reflexive_2110 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2110 :: T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2110 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.RightInverse._.Eq₂.setoid
d_setoid_2112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_Setoid_46
d_setoid_2112 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46 -> T_Setoid_46 -> T_RightInverse_2036 -> T_Setoid_46
du_setoid_2112 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_setoid_2112 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2112 :: T_Setoid_46 -> T_Setoid_46 -> T_RightInverse_2036 -> T_Setoid_46
du_setoid_2112 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.RightInverse._.Eq₂.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2114 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2114 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_sym_2114 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2114 :: T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2114 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.RightInverse._.Eq₂.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2116 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6 = T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2116 T_Setoid_46
v4 T_Setoid_46
v5 T_RightInverse_2036
v6
du_trans_2116 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2116 :: T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2116 T_Setoid_46
v0 T_Setoid_46
v1 T_RightInverse_2036
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsRightInverse_438 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_450 (AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.RightInverse.equivalence
d_equivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_RightInverse_2036 -> T_Equivalence_1858
d_equivalence_2118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_RightInverse_2036
-> T_Equivalence_1858
d_equivalence_2118 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_RightInverse_2036
v6
  = T_RightInverse_2036 -> T_Equivalence_1858
du_equivalence_2118 T_RightInverse_2036
v6
du_equivalence_2118 :: T_RightInverse_2036 -> T_Equivalence_1858
du_equivalence_2118 :: T_RightInverse_2036 -> T_Equivalence_1858
du_equivalence_2118 T_RightInverse_2036
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_1858)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_1858
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_1858
C_constructor_1940 ((T_RightInverse_2036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_to_2048 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v0))
      ((T_RightInverse_2036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_from_2050 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v0)) ((T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2052 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v0))
      ((T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2054 (T_RightInverse_2036 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036
v0))
-- Function.Bundles._.Inverse
d_Inverse_2122 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Inverse_2122 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Inverse_2122
  = C_constructor_2220 (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_2134 :: T_Inverse_2122 -> AgdaAny -> AgdaAny
d_to_2134 :: T_Inverse_2122 -> AgdaAny -> AgdaAny
d_to_2134 T_Inverse_2122
v0
  = case T_Inverse_2122 -> T_Inverse_2122
forall a b. a -> b
coe T_Inverse_2122
v0 of
      C_constructor_2220 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_2122
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.from
d_from_2136 :: T_Inverse_2122 -> AgdaAny -> AgdaAny
d_from_2136 :: T_Inverse_2122 -> AgdaAny -> AgdaAny
d_from_2136 T_Inverse_2122
v0
  = case T_Inverse_2122 -> T_Inverse_2122
forall a b. a -> b
coe T_Inverse_2122
v0 of
      C_constructor_2220 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_2122
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.to-cong
d_to'45'cong_2138 ::
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2138 :: T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2138 T_Inverse_2122
v0
  = case T_Inverse_2122 -> T_Inverse_2122
forall a b. a -> b
coe T_Inverse_2122
v0 of
      C_constructor_2220 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_2122
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.from-cong
d_from'45'cong_2140 ::
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2140 :: T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2140 T_Inverse_2122
v0
  = case T_Inverse_2122 -> T_Inverse_2122
forall a b. a -> b
coe T_Inverse_2122
v0 of
      C_constructor_2220 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_2122
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.inverse
d_inverse_2142 ::
  T_Inverse_2122 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2142 :: T_Inverse_2122 -> T_Σ_14
d_inverse_2142 T_Inverse_2122
v0
  = case T_Inverse_2122 -> T_Inverse_2122
forall a b. a -> b
coe T_Inverse_2122
v0 of
      C_constructor_2220 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_2122
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.inverseˡ
d_inverse'737'_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2144 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_inverse'737'_2144 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Inverse_2122
v6 AgdaAny
v7 AgdaAny
v8
  = T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_2144 T_Inverse_2122
v6 AgdaAny
v7 AgdaAny
v8
du_inverse'737'_2144 ::
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_2144 :: T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_2144 T_Inverse_2122
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_2122 -> T_Σ_14
d_inverse_2142 (T_Inverse_2122 -> T_Inverse_2122
forall a b. a -> b
coe T_Inverse_2122
v0))
      AgdaAny
v1 AgdaAny
v2
-- Function.Bundles._.Inverse.inverseʳ
d_inverse'691'_2146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_inverse'691'_2146 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Inverse_2122
v6 AgdaAny
v7 AgdaAny
v8
  = T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_2146 T_Inverse_2122
v6 AgdaAny
v7 AgdaAny
v8
du_inverse'691'_2146 ::
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_2146 :: T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_2146 T_Inverse_2122
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_2122 -> T_Σ_14
d_inverse_2142 (T_Inverse_2122 -> T_Inverse_2122
forall a b. a -> b
coe T_Inverse_2122
v0))
      AgdaAny
v1 AgdaAny
v2
-- Function.Bundles._.Inverse.leftInverse
d_leftInverse_2148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> T_LeftInverse_1942
d_leftInverse_2148 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_LeftInverse_1942
d_leftInverse_2148 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Inverse_2122 -> T_LeftInverse_1942
du_leftInverse_2148 T_Inverse_2122
v6
du_leftInverse_2148 :: T_Inverse_2122 -> T_LeftInverse_1942
du_leftInverse_2148 :: T_Inverse_2122 -> T_LeftInverse_1942
du_leftInverse_2148 T_Inverse_2122
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_LeftInverse_1942)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_LeftInverse_1942
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1942
C_constructor_2034 ((T_Inverse_2122 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny
d_to_2134 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
      ((T_Inverse_2122 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny
d_from_2136 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0)) ((T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2138 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
      ((T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2140 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
      ((T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'737'_2144 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
-- Function.Bundles._.Inverse.rightInverse
d_rightInverse_2150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> T_RightInverse_2036
d_rightInverse_2150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_RightInverse_2036
d_rightInverse_2150 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Inverse_2122 -> T_RightInverse_2036
du_rightInverse_2150 T_Inverse_2122
v6
du_rightInverse_2150 :: T_Inverse_2122 -> T_RightInverse_2036
du_rightInverse_2150 :: T_Inverse_2122 -> T_RightInverse_2036
du_rightInverse_2150 T_Inverse_2122
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_RightInverse_2036)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_RightInverse_2036
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_RightInverse_2036
C_constructor_2120 ((T_Inverse_2122 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny
d_to_2134 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
      ((T_Inverse_2122 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny
d_from_2136 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0)) ((T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2138 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
      ((T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2140 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
      ((T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_2146 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v0))
-- Function.Bundles._.Inverse._.isLeftInverse
d_isLeftInverse_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
d_isLeftInverse_2154 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_IsLeftInverse_346
d_isLeftInverse_2154 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsLeftInverse_346
du_isLeftInverse_2154 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_isLeftInverse_2154 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
du_isLeftInverse_2154 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsLeftInverse_346
du_isLeftInverse_2154 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe
      T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
      ((T_Inverse_2122 -> T_LeftInverse_1942) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> T_LeftInverse_1942
du_leftInverse_2148 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2))
-- Function.Bundles._.Inverse._.strictlyInverseˡ
d_strictlyInverse'737'_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_2156 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_2156 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2156 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_strictlyInverse'737'_2156 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2156 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2156 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Inverse_2122 -> T_LeftInverse_1942) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> T_LeftInverse_1942
du_leftInverse_2148 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_424
         ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
         ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Inverse._.isRightInverse
d_isRightInverse_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438
d_isRightInverse_2160 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_IsRightInverse_438
d_isRightInverse_2160 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Inverse_2122 -> T_IsRightInverse_438
du_isRightInverse_2160 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_isRightInverse_2160 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_438
du_isRightInverse_2160 :: T_Setoid_46
-> T_Setoid_46 -> T_Inverse_2122 -> T_IsRightInverse_438
du_isRightInverse_2160 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = (T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe
      T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
      ((T_Inverse_2122 -> T_RightInverse_2036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> T_RightInverse_2036
du_rightInverse_2150 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2))
-- Function.Bundles._.Inverse._.strictlyInverseʳ
d_strictlyInverse'691'_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_2162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_2162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2162 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_strictlyInverse'691'_2162 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2162 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_2162 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Inverse_2122 -> T_RightInverse_2036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> T_RightInverse_2036
du_rightInverse_2150 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'691'_516
         ((T_RightInverse_2036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_2036 -> AgdaAny -> AgdaAny
d_to_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
         ((T_Setoid_46
 -> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_RightInverse_2036 -> T_IsRightInverse_438
du_isRightInverse_2060 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.Inverse.isInverse
d_isInverse_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> MAlonzo.Code.Function.Structures.T_IsInverse_526
d_isInverse_2164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_IsInverse_526
d_isInverse_2164 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_isInverse_2164 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> MAlonzo.Code.Function.Structures.T_IsInverse_526
du_isInverse_2164 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = (T_IsLeftInverse_346
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe
      T_IsLeftInverse_346
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInverse_526
MAlonzo.Code.Function.Structures.C_constructor_618
      ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1)
         ((T_Inverse_2122 -> T_LeftInverse_1942) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> T_LeftInverse_1942
du_leftInverse_2148 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2)))
      ((T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_inverse'691'_2146 (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2))
-- Function.Bundles._.Inverse._.Eq₁._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2170 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2172 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2172 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁.Carrier
d_Carrier_2174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> ()
d_Carrier_2174 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_Level_18
d_Carrier_2174 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁.isEquivalence
d_isEquivalence_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2176 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_IsEquivalence_28
d_isEquivalence_2176 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsEquivalence_28
du_isEquivalence_2176 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_isEquivalence_2176 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2176 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsEquivalence_28
du_isEquivalence_2176 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2178 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2178 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Inverse_2122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2178 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_isPartialEquivalence_2178 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2178 :: T_Setoid_46
-> T_Setoid_46 -> T_Inverse_2122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2178 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Inverse._.Eq₁.partialSetoid
d_partialSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_PartialSetoid_10
d_partialSetoid_2180 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_PartialSetoid_10
du_partialSetoid_2180 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_partialSetoid_2180 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2180 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_PartialSetoid_10
du_partialSetoid_2180 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
               ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_2182 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_RawSetoid_12
d_rawSetoid_2182 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁.refl
d_refl_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
d_refl_2184 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
d_refl_2184 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_refl_2184 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_refl_2184 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
du_refl_2184 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_refl_2184 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
               ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_28
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_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2186 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2186 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2186 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_reflexive_2186 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2186 :: T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2186 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Inverse._.Eq₁.setoid
d_setoid_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2188 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_Setoid_46
d_setoid_2188 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_Setoid_46
du_setoid_2188 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_setoid_2188 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2188 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_Setoid_46
du_setoid_2188 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
            ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v4))))
-- Function.Bundles._.Inverse._.Eq₁.sym
d_sym_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2190 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_sym_2190 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2190 :: T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2190 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Inverse._.Eq₁.trans
d_trans_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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2192 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2192 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_trans_2192 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2192 :: T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2192 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Inverse._.Eq₂._≈_
d__'8776'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2196 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2196 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂._≉_
d__'8777'__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_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2198 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂.Carrier
d_Carrier_2200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> ()
d_Carrier_2200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_Level_18
d_Carrier_2200 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂.isEquivalence
d_isEquivalence_2202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_IsEquivalence_28
d_isEquivalence_2202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsEquivalence_28
du_isEquivalence_2202 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_isEquivalence_2202 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2202 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsEquivalence_28
du_isEquivalence_2202 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_2204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2204 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2204 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_Inverse_2122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2204 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_isPartialEquivalence_2204 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2204 :: T_Setoid_46
-> T_Setoid_46 -> T_Inverse_2122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2204 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Inverse._.Eq₂.partialSetoid
d_partialSetoid_2206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2206 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_PartialSetoid_10
d_partialSetoid_2206 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_PartialSetoid_10
du_partialSetoid_2206 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_partialSetoid_2206 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2206 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_PartialSetoid_10
du_partialSetoid_2206 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
               ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₂.rawSetoid
d_rawSetoid_2208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_2208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_RawSetoid_12
d_rawSetoid_2208 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂.refl
d_refl_2210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
d_refl_2210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
d_refl_2210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_refl_2210 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_refl_2210 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny
du_refl_2210 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> AgdaAny -> AgdaAny
du_refl_2210 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
               ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_28
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_2212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2212 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2212 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2212 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_reflexive_2212 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2212 :: T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2212 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Inverse._.Eq₂.setoid
d_setoid_2214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2214 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> T_Setoid_46
d_setoid_2214 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_Setoid_46
du_setoid_2214 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_setoid_2214 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2214 :: T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_Setoid_46
du_setoid_2214 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
            ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v4))))
-- Function.Bundles._.Inverse._.Eq₂.sym
d_sym_2216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2216 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2216 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_sym_2216 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2216 :: T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2216 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.Inverse._.Eq₂.trans
d_trans_2218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2218 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2218 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6 = T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2218 T_Setoid_46
v4 T_Setoid_46
v5 T_Inverse_2122
v6
du_trans_2218 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_Inverse_2122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2218 :: T_Setoid_46
-> T_Setoid_46
-> T_Inverse_2122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2218 T_Setoid_46
v0 T_Setoid_46
v1 T_Inverse_2122
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_Inverse_2122 -> T_IsInverse_526
du_isInverse_2164 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_Inverse_2122 -> AgdaAny
forall a b. a -> b
coe T_Inverse_2122
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_346
v4
             = T_IsInverse_526 -> T_IsLeftInverse_346
MAlonzo.Code.Function.Structures.d_isLeftInverse_536 (AgdaAny -> T_IsInverse_526
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: AgdaAny
v6
                   = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))
-- Function.Bundles._.BiEquivalence
d_BiEquivalence_2222 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_BiEquivalence_2222 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_BiEquivalence_2222
  = C_constructor_2248 (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.BiEquivalence.to
d_to_2236 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny
d_to_2236 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny
d_to_2236 T_BiEquivalence_2222
v0
  = case T_BiEquivalence_2222 -> T_BiEquivalence_2222
forall a b. a -> b
coe T_BiEquivalence_2222
v0 of
      C_constructor_2248 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_2222
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₁
d_from'8321'_2238 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny
d_from'8321'_2238 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny
d_from'8321'_2238 T_BiEquivalence_2222
v0
  = case T_BiEquivalence_2222 -> T_BiEquivalence_2222
forall a b. a -> b
coe T_BiEquivalence_2222
v0 of
      C_constructor_2248 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_2222
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₂
d_from'8322'_2240 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny
d_from'8322'_2240 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny
d_from'8322'_2240 T_BiEquivalence_2222
v0
  = case T_BiEquivalence_2222 -> T_BiEquivalence_2222
forall a b. a -> b
coe T_BiEquivalence_2222
v0 of
      C_constructor_2248 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_2222
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.to-cong
d_to'45'cong_2242 ::
  T_BiEquivalence_2222 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2242 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2242 T_BiEquivalence_2222
v0
  = case T_BiEquivalence_2222 -> T_BiEquivalence_2222
forall a b. a -> b
coe T_BiEquivalence_2222
v0 of
      C_constructor_2248 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_2222
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₁-cong
d_from'8321''45'cong_2244 ::
  T_BiEquivalence_2222 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2244 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2244 T_BiEquivalence_2222
v0
  = case T_BiEquivalence_2222 -> T_BiEquivalence_2222
forall a b. a -> b
coe T_BiEquivalence_2222
v0 of
      C_constructor_2248 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_2222
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.from₂-cong
d_from'8322''45'cong_2246 ::
  T_BiEquivalence_2222 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2246 :: T_BiEquivalence_2222 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2246 T_BiEquivalence_2222
v0
  = case T_BiEquivalence_2222 -> T_BiEquivalence_2222
forall a b. a -> b
coe T_BiEquivalence_2222
v0 of
      C_constructor_2248 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_2222
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse
d_BiInverse_2250 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_BiInverse_2250 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_BiInverse_2250
  = C_constructor_2290 (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_2268 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_to_2268 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_to_2268 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₁
d_from'8321'_2270 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_from'8321'_2270 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_from'8321'_2270 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₂
d_from'8322'_2272 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_from'8322'_2272 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_from'8322'_2272 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.to-cong
d_to'45'cong_2274 ::
  T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2274 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2274 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₁-cong
d_from'8321''45'cong_2276 ::
  T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2276 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2276 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.from₂-cong
d_from'8322''45'cong_2278 ::
  T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2278 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2278 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.inverseˡ
d_inverse'737'_2280 ::
  T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2280 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2280 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.inverseʳ
d_inverse'691'_2282 ::
  T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2282 :: T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2282 T_BiInverse_2250
v0
  = case T_BiInverse_2250 -> T_BiInverse_2250
forall a b. a -> b
coe T_BiInverse_2250
v0 of
      C_constructor_2290 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_2250
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.to-isCongruent
d_to'45'isCongruent_2284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_BiInverse_2250 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_to'45'isCongruent_2284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_BiInverse_2250
-> T_IsCongruent_22
d_to'45'isCongruent_2284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_BiInverse_2250
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_BiInverse_2250 -> T_IsCongruent_22
du_to'45'isCongruent_2284 T_Setoid_46
v4 T_Setoid_46
v5 T_BiInverse_2250
v6
du_to'45'isCongruent_2284 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_BiInverse_2250 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_to'45'isCongruent_2284 :: T_Setoid_46 -> T_Setoid_46 -> T_BiInverse_2250 -> T_IsCongruent_22
du_to'45'isCongruent_2284 T_Setoid_46
v0 T_Setoid_46
v1 T_BiInverse_2250
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> T_IsEquivalence_28 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_constructor_94
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2274 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v2))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0))
      ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1))
-- Function.Bundles._.BiInverse.isBiInverse
d_isBiInverse_2286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_BiInverse_2250 ->
  MAlonzo.Code.Function.Structures.T_IsBiInverse_714
d_isBiInverse_2286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_BiInverse_2250
-> T_IsBiInverse_714
d_isBiInverse_2286 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_BiInverse_2250
v6
  = T_Setoid_46 -> T_Setoid_46 -> T_BiInverse_2250 -> T_IsBiInverse_714
du_isBiInverse_2286 T_Setoid_46
v4 T_Setoid_46
v5 T_BiInverse_2250
v6
du_isBiInverse_2286 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_BiInverse_2250 ->
  MAlonzo.Code.Function.Structures.T_IsBiInverse_714
du_isBiInverse_2286 :: T_Setoid_46 -> T_Setoid_46 -> T_BiInverse_2250 -> T_IsBiInverse_714
du_isBiInverse_2286 T_Setoid_46
v0 T_Setoid_46
v1 T_BiInverse_2250
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsBiInverse_714)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsBiInverse_714
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_714
MAlonzo.Code.Function.Structures.C_constructor_802
      ((T_Setoid_46
 -> T_Setoid_46 -> T_BiInverse_2250 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46 -> T_Setoid_46 -> T_BiInverse_2250 -> T_IsCongruent_22
du_to'45'isCongruent_2284 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v2))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2276 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v2))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2278 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v2))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2280 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v2))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_2282 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v2))
-- Function.Bundles._.BiInverse.biEquivalence
d_biEquivalence_2288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_BiInverse_2250 -> T_BiEquivalence_2222
d_biEquivalence_2288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_BiInverse_2250
-> T_BiEquivalence_2222
d_biEquivalence_2288 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_BiInverse_2250
v6
  = T_BiInverse_2250 -> T_BiEquivalence_2222
du_biEquivalence_2288 T_BiInverse_2250
v6
du_biEquivalence_2288 :: T_BiInverse_2250 -> T_BiEquivalence_2222
du_biEquivalence_2288 :: T_BiInverse_2250 -> T_BiEquivalence_2222
du_biEquivalence_2288 T_BiInverse_2250
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_BiEquivalence_2222)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_BiEquivalence_2222
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_2222
C_constructor_2248 ((T_BiInverse_2250 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_to_2268 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v0))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_from'8321'_2270 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v0)) ((T_BiInverse_2250 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny
d_from'8322'_2272 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v0))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2274 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v0))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_2276 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v0))
      ((T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_2278 (T_BiInverse_2250 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_2250
v0))
-- Function.Bundles._.SplitSurjection
d_SplitSurjection_2292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 -> ()
d_SplitSurjection_2292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
d_SplitSurjection_2292 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.equivalence
d_equivalence_2298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> T_Equivalence_1858
d_equivalence_2298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Equivalence_1858
d_equivalence_2298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_LeftInverse_1942 -> T_Equivalence_1858
du_equivalence_2298 T_LeftInverse_1942
v6
du_equivalence_2298 :: T_LeftInverse_1942 -> T_Equivalence_1858
du_equivalence_2298 :: T_LeftInverse_1942 -> T_Equivalence_1858
du_equivalence_2298 T_LeftInverse_1942
v0 = (T_LeftInverse_1942 -> T_Equivalence_1858)
-> AgdaAny -> T_Equivalence_1858
forall a b. a -> b
coe T_LeftInverse_1942 -> T_Equivalence_1858
du_equivalence_2026 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)
-- Function.Bundles._.SplitSurjection.from
d_from_2300 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_2300 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_2300 T_LeftInverse_1942
v0 = (T_LeftInverse_1942 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)
-- Function.Bundles._.SplitSurjection.from-cong
d_from'45'cong_2302 ::
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2302 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_2302 T_LeftInverse_1942
v0 = (T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_1960 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)
-- Function.Bundles._.SplitSurjection.inverseˡ
d_inverse'737'_2304 ::
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2304 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_2304 T_LeftInverse_1942
v0 = (T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_1962 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)
-- Function.Bundles._.SplitSurjection.isCongruent
d_isCongruent_2306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_2306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsCongruent_22
d_isCongruent_2306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22
du_isCongruent_2306 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isCongruent_2306 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_2306 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22
du_isCongruent_2306 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsCongruent_22
du_isCongruent_1964 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2)
-- Function.Bundles._.SplitSurjection.isLeftInverse
d_isLeftInverse_2308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
d_isLeftInverse_2308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsLeftInverse_346
d_isLeftInverse_2308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_2308 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isLeftInverse_2308 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_346
du_isLeftInverse_2308 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_2308 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2)
-- Function.Bundles._.SplitSurjection.isSplitSurjection
d_isSplitSurjection_2310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_806
d_isSplitSurjection_2310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsSplitSurjection_806
d_isSplitSurjection_2310 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSplitSurjection_806
du_isSplitSurjection_2310 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isSplitSurjection_2310 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSplitSurjection_806
du_isSplitSurjection_2310 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSplitSurjection_806
du_isSplitSurjection_2310 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSplitSurjection_806)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSplitSurjection_806
du_isSplitSurjection_2028 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2)
-- Function.Bundles._.SplitSurjection.isSurjection
d_isSurjection_2312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
d_isSurjection_2312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsSurjection_174
d_isSurjection_2312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSurjection_174
du_isSurjection_2312 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isSurjection_2312 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_174
du_isSurjection_2312 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsSurjection_174
du_isSurjection_2312 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
MAlonzo.Code.Function.Structures.du_isSurjection_428
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
-- Function.Bundles._.SplitSurjection.strictlyInverseˡ
d_strictlyInverse'737'_2314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_2314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_2314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2314 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_strictlyInverse'737'_2314 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2314 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_2314 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Structures.du_strictlyInverse'737'_424
      ((T_LeftInverse_1942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_from_1956 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
      ((T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2))
-- Function.Bundles._.SplitSurjection.surjection
d_surjection_2316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> T_Surjection_918
d_surjection_2316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Surjection_918
d_surjection_2316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_46
v4 ~T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_LeftInverse_1942 -> T_Surjection_918
du_surjection_2316 T_LeftInverse_1942
v6
du_surjection_2316 :: T_LeftInverse_1942 -> T_Surjection_918
du_surjection_2316 :: T_LeftInverse_1942 -> T_Surjection_918
du_surjection_2316 T_LeftInverse_1942
v0 = (T_LeftInverse_1942 -> T_Surjection_918)
-> AgdaAny -> T_Surjection_918
forall a b. a -> b
coe T_LeftInverse_1942 -> T_Surjection_918
du_surjection_2030 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)
-- Function.Bundles._.SplitSurjection.to
d_to_2318 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_to_2318 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_to_2318 T_LeftInverse_1942
v0 = (T_LeftInverse_1942 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_to_1954 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)
-- Function.Bundles._.SplitSurjection.to-cong
d_to'45'cong_2320 ::
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2320 :: T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_2320 T_LeftInverse_1942
v0 = (T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'cong_1958 (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v0)
-- Function.Bundles._.SplitSurjection.Eq₁._≈_
d__'8776'__2324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2324 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₁._≉_
d__'8777'__2326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2326 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₁.Carrier
d_Carrier_2328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> ()
d_Carrier_2328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
d_Carrier_2328 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₁.isEquivalence
d_isEquivalence_2330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsEquivalence_28
d_isEquivalence_2330 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_2330 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isEquivalence_2330 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2330 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_2330 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_2332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2332 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2332 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isPartialEquivalence_2332 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2332 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2332 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₁.partialSetoid
d_partialSetoid_2334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_PartialSetoid_10
d_partialSetoid_2334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_2334 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_partialSetoid_2334 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2334 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_2334 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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.rawSetoid
d_rawSetoid_2336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_2336 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
d_rawSetoid_2336 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₁.refl
d_refl_2338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_refl_2338 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
d_refl_2338 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2338 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_refl_2338 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2338 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2338 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_2340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2340 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_reflexive_2340 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2340 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2340 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.SplitSurjection.Eq₁.setoid
d_setoid_2342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2342 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Setoid_46
d_setoid_2342 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_2342 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_setoid_2342 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2342 :: T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_2342 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.SplitSurjection.Eq₁.sym
d_sym_2344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2344 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2344 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_sym_2344 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2344 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2344 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₁.trans
d_trans_2346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2346 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_trans_2346 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2346 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2346 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₂._≈_
d__'8776'__2350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2350 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₂._≉_
d__'8777'__2352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2352 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__2352 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₂.Carrier
d_Carrier_2354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> ()
d_Carrier_2354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
d_Carrier_2354 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₂.isEquivalence
d_isEquivalence_2356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsEquivalence_28
d_isEquivalence_2356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_2356 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isEquivalence_2356 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2356 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsEquivalence_28
du_isEquivalence_2356 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_28
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_2358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2358 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2358 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2358 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_isPartialEquivalence_2358 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2358 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2358 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₂.partialSetoid
d_partialSetoid_2360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2360 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_PartialSetoid_10
d_partialSetoid_2360 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_2360 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_partialSetoid_2360 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2360 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_PartialSetoid_10
du_partialSetoid_2360 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v4))))
-- Function.Bundles._.SplitSurjection.Eq₂.rawSetoid
d_rawSetoid_2362 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_2362 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
d_rawSetoid_2362 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_RawSetoid_12
forall a. a
erased
-- Function.Bundles._.SplitSurjection.Eq₂.refl
d_refl_2364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
d_refl_2364 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
d_refl_2364 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2364 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_refl_2364 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2364 :: T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> AgdaAny -> AgdaAny
du_refl_2364 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_28
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_2366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2366 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2366 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
  = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2366 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_reflexive_2366 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2366 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_2366 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.SplitSurjection.Eq₂.setoid
d_setoid_2368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2368 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> T_Setoid_46
d_setoid_2368 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_2368 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_setoid_2368 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2368 :: T_Setoid_46 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_Setoid_46
du_setoid_2368 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68
         ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Function.Bundles._.SplitSurjection.Eq₂.sym
d_sym_2370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2370 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2370 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_sym_2370 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2370 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_2370 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._.SplitSurjection.Eq₂.trans
d_trans_2372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2372 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2372 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6 = T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2372 T_Setoid_46
v4 T_Setoid_46
v5 T_LeftInverse_1942
v6
du_trans_2372 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  T_LeftInverse_1942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2372 :: T_Setoid_46
-> T_Setoid_46
-> T_LeftInverse_1942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_2372 T_Setoid_46
v0 T_Setoid_46
v1 T_LeftInverse_1942
v2
  = let v3 :: AgdaAny
v3 = (T_Setoid_46
 -> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
-> T_Setoid_46 -> T_LeftInverse_1942 -> T_IsLeftInverse_346
du_isLeftInverse_1966 (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v0) (T_Setoid_46 -> AgdaAny
forall a b. a -> b
coe T_Setoid_46
v1) (T_LeftInverse_1942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_1942
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsCongruent_22
v4
             = T_IsLeftInverse_346 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_358 (AgdaAny -> T_IsLeftInverse_346
forall a b. a -> b
coe AgdaAny
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: AgdaAny
v5
                = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
MAlonzo.Code.Function.Structures.du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))
-- Function.Bundles._⟶ₛ_
d__'10230''8347'__2374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46 -> ()
d__'10230''8347'__2374 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
d__'10230''8347'__2374 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_46
-> T_Setoid_46
-> T_Level_18
forall a. a
erased
-- Function.Bundles._⟶_
d__'10230'__2376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'10230'__2376 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'10230'__2376 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↣_
d__'8611'__2382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8611'__2382 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8611'__2382 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↠_
d__'8608'__2388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8608'__2388 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8608'__2388 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._⤖_
d__'10518'__2394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'10518'__2394 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'10518'__2394 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._⇔_
d__'8660'__2400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8660'__2400 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8660'__2400 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↩_
d__'8617'__2406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8617'__2406 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8617'__2406 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↪_
d__'8618'__2412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8618'__2412 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8618'__2412 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↩↪_
d__'8617''8618'__2418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8617''8618'__2418 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8617''8618'__2418 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↔_
d__'8596'__2424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8596'__2424 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8596'__2424 = 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'_2442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> () -> (AgdaAny -> AgdaAny) -> T_Func_774
d_mk'10230'_2442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Func_774
d_mk'10230'_2442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 = (AgdaAny -> AgdaAny) -> T_Func_774
du_mk'10230'_2442 AgdaAny -> AgdaAny
v4
du_mk'10230'_2442 :: (AgdaAny -> AgdaAny) -> T_Func_774
du_mk'10230'_2442 :: (AgdaAny -> AgdaAny) -> T_Func_774
du_mk'10230'_2442 AgdaAny -> AgdaAny
v0 = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774)
-> AgdaAny -> AgdaAny -> T_Func_774
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_774
C_constructor_840 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased
-- Function.Bundles._.mk↣
d_mk'8611'_2448 ::
  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_842
d_mk'8611'_2448 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_842
d_mk'8611'_2448 ~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_842
du_mk'8611'_2448 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v5
du_mk'8611'_2448 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Injection_842
du_mk'8611'_2448 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_842
du_mk'8611'_2448 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Injection_842)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Injection_842
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Injection_842
C_constructor_916 ((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'_2456 ::
  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_918
d_mk'8608'_2456 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_918
d_mk'8608'_2456 ~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_918
du_mk'8608'_2456 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5
du_mk'8608'_2456 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_918
du_mk'8608'_2456 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_918
du_mk'8608'_2456 AgdaAny -> AgdaAny
v0 AgdaAny -> T_Σ_14
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_918)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_918
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_918
C_constructor_1002 ((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'_2464 ::
  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_1004
d_mk'10518'_2464 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Bijection_1004
d_mk'10518'_2464 ~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_1004
du_mk'10518'_2464 AgdaAny -> AgdaAny
v4 T_Σ_14
v5
du_mk'10518'_2464 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Bijection_1004
du_mk'10518'_2464 :: (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Bijection_1004
du_mk'10518'_2464 AgdaAny -> AgdaAny
v0 T_Σ_14
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Bijection_1004)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Bijection_1004
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Bijection_1004
C_constructor_1094 ((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'_2474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_1858
d_mk'8660'_2474 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Equivalence_1858
d_mk'8660'_2474 ~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_1858
du_mk'8660'_2474 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5
du_mk'8660'_2474 ::
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_1858
du_mk'8660'_2474 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_1858
du_mk'8660'_2474 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_1858)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_1858
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_1858
C_constructor_1940 ((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'_2484 ::
  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_1942
d_mk'8617'_2484 :: 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_1942
d_mk'8617'_2484 ~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_1942
du_mk'8617'_2484 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v6
du_mk'8617'_2484 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_LeftInverse_1942
du_mk'8617'_2484 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_LeftInverse_1942
du_mk'8617'_2484 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_1942)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_LeftInverse_1942
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_LeftInverse_1942
C_constructor_2034 ((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'_2496 ::
  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_2036
d_mk'8618'_2496 :: 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_2036
d_mk'8618'_2496 ~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_2036
du_mk'8618'_2496 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v6
du_mk'8618'_2496 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_RightInverse_2036
du_mk'8618'_2496 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_RightInverse_2036
du_mk'8618'_2496 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_2036)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_RightInverse_2036
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_RightInverse_2036
C_constructor_2120 ((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'_2510 ::
  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_2250
d_mk'8617''8618'_2510 :: 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_2250
d_mk'8617''8618'_2510 ~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_2250
du_mk'8617''8618'_2510 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'_2510 ::
  (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_2250
du_mk'8617''8618'_2510 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_BiInverse_2250
du_mk'8617''8618'_2510 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_2250)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_BiInverse_2250
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_2250
C_constructor_2290 ((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'_2526 ::
  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_2122
d_mk'8596'_2526 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Inverse_2122
d_mk'8596'_2526 ~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_2122
du_mk'8596'_2526 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_Σ_14
v6
du_mk'8596'_2526 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Inverse_2122
du_mk'8596'_2526 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_2122
du_mk'8596'_2526 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_2122)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_Inverse_2122
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Inverse_2122
C_constructor_2220 ((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'_2536 ::
  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_918
d_mk'8608''8347'_2536 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_918
d_mk'8608''8347'_2536 ~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_918
du_mk'8608''8347'_2536 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5
du_mk'8608''8347'_2536 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_918
du_mk'8608''8347'_2536 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_918
du_mk'8608''8347'_2536 AgdaAny -> AgdaAny
v0 AgdaAny -> T_Σ_14
v1
  = ((AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_918)
-> AgdaAny -> AgdaAny -> T_Surjection_918
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_918
du_mk'8608'_2456 ((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'_2542 ::
  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_2122
d_mk'8596''8347''8242'_2542 :: 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_2122
d_mk'8596''8347''8242'_2542 ~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_2122
du_mk'8596''8347''8242'_2542 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5
du_mk'8596''8347''8242'_2542 ::
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Inverse_2122
du_mk'8596''8347''8242'_2542 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Inverse_2122
du_mk'8596''8347''8242'_2542 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_2122)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Inverse_2122
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_2122
du_mk'8596'_2526 ((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'__2568 :: T_Func_774 -> AgdaAny -> AgdaAny
d__'10216''36''10217'__2568 :: T_Func_774 -> AgdaAny -> AgdaAny
d__'10216''36''10217'__2568 T_Func_774
v0 = (T_Func_774 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Func_774 -> AgdaAny -> AgdaAny
d_to_780 (T_Func_774 -> AgdaAny
forall a b. a -> b
coe T_Func_774
v0)