{-# 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.Metric.Structures where

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

-- Function.Metric.Structures.IsProtoMetric
d_IsProtoMetric_30 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsProtoMetric_30 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 p
a11 = ()
data T_IsProtoMetric_30
  = C_IsProtoMetric'46'constructor_2109 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
                                        MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                        (AgdaAny ->
                                         AgdaAny ->
                                         AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsProtoMetric.isPartialOrder
d_isPartialOrder_42 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_42 :: T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 T_IsProtoMetric_30
v0
  = case T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0 of
      C_IsProtoMetric'46'constructor_2109 T_IsPartialOrder_162
v1 T_IsEquivalence_26
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v1
      T_IsProtoMetric_30
_ -> T_IsPartialOrder_162
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsProtoMetric.≈-isEquivalence
d_'8776''45'isEquivalence_44 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_44 :: T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 T_IsProtoMetric_30
v0
  = case T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0 of
      C_IsProtoMetric'46'constructor_2109 T_IsPartialOrder_162
v1 T_IsEquivalence_26
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v2
      T_IsProtoMetric_30
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsProtoMetric.cong
d_cong_46 ::
  T_IsProtoMetric_30 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_46 :: T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_46 T_IsProtoMetric_30
v0
  = case T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0 of
      C_IsProtoMetric'46'constructor_2109 T_IsPartialOrder_162
v1 T_IsEquivalence_26
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsProtoMetric_30
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsProtoMetric.nonNegative
d_nonNegative_48 ::
  T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_48 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_48 T_IsProtoMetric_30
v0
  = case T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0 of
      C_IsProtoMetric'46'constructor_2109 T_IsPartialOrder_162
v1 T_IsEquivalence_26
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsProtoMetric_30
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsProtoMetric._.antisym
d_antisym_52 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_52 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_52 T_IsProtoMetric_30
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))
-- Function.Metric.Structures.IsProtoMetric._.isEquivalence
d_isEquivalence_54 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_54 :: T_IsProtoMetric_30 -> T_IsEquivalence_26
d_isEquivalence_54 T_IsProtoMetric_30
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0)))
-- Function.Metric.Structures.IsProtoMetric._.isPreorder
d_isPreorder_56 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_56 :: T_IsProtoMetric_30 -> T_IsPreorder_70
d_isPreorder_56 T_IsProtoMetric_30
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))
-- Function.Metric.Structures.IsProtoMetric._.refl
d_refl_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_58 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
d_refl_58 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
du_refl_58 T_IsProtoMetric_30
v12
du_refl_58 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
du_refl_58 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
du_refl_58 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Function.Metric.Structures.IsProtoMetric._.reflexive
d_reflexive_60 ::
  T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_60 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_60 T_IsProtoMetric_30
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0)))
-- Function.Metric.Structures.IsProtoMetric._.trans
d_trans_62 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_62 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_62 T_IsProtoMetric_30
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0)))
-- Function.Metric.Structures.IsProtoMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_64 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_64 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> T_Σ_14
d_'8764''45'resp'45''8776'_64 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                              ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30 -> T_Σ_14
du_'8764''45'resp'45''8776'_64 T_IsProtoMetric_30
v12
du_'8764''45'resp'45''8776'_64 ::
  T_IsProtoMetric_30 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_64 :: T_IsProtoMetric_30 -> T_Σ_14
du_'8764''45'resp'45''8776'_64 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Function.Metric.Structures.IsProtoMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_66 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_66 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                   ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_66 T_IsProtoMetric_30
v12
du_'8764''45'resp'691''45''8776'_66 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_66 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_66 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Function.Metric.Structures.IsProtoMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_68 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_68 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_68 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                   ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_68 T_IsProtoMetric_30
v12
du_'8764''45'resp'737''45''8776'_68 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_68 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_68 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Function.Metric.Structures.IsProtoMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_72 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_72 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_72 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                          ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_72 T_IsProtoMetric_30
v12
du_isPartialEquivalence_72 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_72 :: T_IsProtoMetric_30 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_72 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
               (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))))
-- Function.Metric.Structures.IsProtoMetric._.Eq.refl
d_refl_74 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_74 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_74 T_IsProtoMetric_30
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))))
-- Function.Metric.Structures.IsProtoMetric._.Eq.reflexive
d_reflexive_76 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_76 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_76 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
               T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_76 T_IsProtoMetric_30
v12
du_reflexive_76 ::
  T_IsProtoMetric_30 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_76 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_76 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                 (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))
              AgdaAny
v3))
-- Function.Metric.Structures.IsProtoMetric._.Eq.sym
d_sym_78 ::
  T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_78 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_78 T_IsProtoMetric_30
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))))
-- Function.Metric.Structures.IsProtoMetric._.Eq.trans
d_trans_80 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_80 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_80 T_IsProtoMetric_30
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))))
-- Function.Metric.Structures.IsProtoMetric.EqC.isPartialEquivalence
d_isPartialEquivalence_84 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_84 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_84 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                          ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_84 T_IsProtoMetric_30
v12
du_isPartialEquivalence_84 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_84 :: T_IsProtoMetric_30 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_84 T_IsProtoMetric_30
v0
  = (T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))
-- Function.Metric.Structures.IsProtoMetric.EqC.refl
d_refl_86 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_86 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_86 T_IsProtoMetric_30
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))
-- Function.Metric.Structures.IsProtoMetric.EqC.reflexive
d_reflexive_88 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsProtoMetric_30 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_88 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_88 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
               T_IsProtoMetric_30
v12
  = T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_88 T_IsProtoMetric_30
v12
du_reflexive_88 ::
  T_IsProtoMetric_30 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_88 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_88 T_IsProtoMetric_30
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0)) AgdaAny
v1
-- Function.Metric.Structures.IsProtoMetric.EqC.sym
d_sym_90 ::
  T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_90 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_90 T_IsProtoMetric_30
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))
-- Function.Metric.Structures.IsProtoMetric.EqC.trans
d_trans_92 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_92 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_92 T_IsProtoMetric_30
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v0))
-- Function.Metric.Structures.IsPreMetric
d_IsPreMetric_96 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsPreMetric_96 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 p
a11 = ()
data T_IsPreMetric_96
  = C_IsPreMetric'46'constructor_6061 T_IsProtoMetric_30
                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsPreMetric.isProtoMetric
d_isProtoMetric_104 :: T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 :: T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 T_IsPreMetric_96
v0
  = case T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0 of
      C_IsPreMetric'46'constructor_6061 T_IsProtoMetric_30
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v1
      T_IsPreMetric_96
_ -> T_IsProtoMetric_30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsPreMetric.≈⇒0
d_'8776''8658'0_106 ::
  T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_106 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_106 T_IsPreMetric_96
v0
  = case T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0 of
      C_IsPreMetric'46'constructor_6061 T_IsProtoMetric_30
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_IsPreMetric_96
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsPreMetric._.antisym
d_antisym_110 ::
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_110 :: T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_110 T_IsPreMetric_96
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))
-- Function.Metric.Structures.IsPreMetric._.cong
d_cong_112 ::
  T_IsPreMetric_96 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_112 :: T_IsPreMetric_96
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_112 T_IsPreMetric_96
v0 = (T_IsProtoMetric_30
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_46 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0))
-- Function.Metric.Structures.IsPreMetric._.isEquivalence
d_isEquivalence_114 ::
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_114 :: T_IsPreMetric_96 -> T_IsEquivalence_26
d_isEquivalence_114 T_IsPreMetric_96
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0))))
-- Function.Metric.Structures.IsPreMetric._.isPartialOrder
d_isPartialOrder_116 ::
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_116 :: T_IsPreMetric_96 -> T_IsPartialOrder_162
d_isPartialOrder_116 T_IsPreMetric_96
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0))
-- Function.Metric.Structures.IsPreMetric._.isPreorder
d_isPreorder_118 ::
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_118 :: T_IsPreMetric_96 -> T_IsPreorder_70
d_isPreorder_118 T_IsPreMetric_96
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))
-- Function.Metric.Structures.IsPreMetric._.nonNegative
d_nonNegative_120 ::
  T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_120 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_120 T_IsPreMetric_96
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_48 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0))
-- Function.Metric.Structures.IsPreMetric._.refl
d_refl_122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 -> AgdaAny -> AgdaAny
d_refl_122 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> AgdaAny
-> AgdaAny
d_refl_122 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_96
v12
  = T_IsPreMetric_96 -> AgdaAny -> AgdaAny
du_refl_122 T_IsPreMetric_96
v12
du_refl_122 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny
du_refl_122 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny
du_refl_122 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.Structures.IsPreMetric._.reflexive
d_reflexive_124 ::
  T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_124 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_124 T_IsPreMetric_96
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0))))
-- Function.Metric.Structures.IsPreMetric._.trans
d_trans_126 ::
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_126 :: T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_126 T_IsPreMetric_96
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0))))
-- Function.Metric.Structures.IsPreMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_128 ::
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_128 :: T_IsPreMetric_96 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_128 T_IsPreMetric_96
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0))
-- Function.Metric.Structures.IsPreMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_130 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> T_Σ_14
d_'8764''45'resp'45''8776'_130 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_96
v12
  = T_IsPreMetric_96 -> T_Σ_14
du_'8764''45'resp'45''8776'_130 T_IsPreMetric_96
v12
du_'8764''45'resp'45''8776'_130 ::
  T_IsPreMetric_96 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_130 :: T_IsPreMetric_96 -> T_Σ_14
du_'8764''45'resp'45''8776'_130 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.Structures.IsPreMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_132 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_132 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_96
v12
  = T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_132 T_IsPreMetric_96
v12
du_'8764''45'resp'691''45''8776'_132 ::
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_132 :: T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_132 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.Structures.IsPreMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_134 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_134 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_96
v12
  = T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_134 T_IsPreMetric_96
v12
du_'8764''45'resp'737''45''8776'_134 ::
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_134 :: T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_134 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.Structures.IsPreMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_138 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_138 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_96
v12
  = T_IsPreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_138 T_IsPreMetric_96
v12
du_isPartialEquivalence_138 ::
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_138 :: T_IsPreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_138 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v1)))
-- Function.Metric.Structures.IsPreMetric._.EqC.refl
d_refl_140 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny
d_refl_140 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny
d_refl_140 T_IsPreMetric_96
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))
-- Function.Metric.Structures.IsPreMetric._.EqC.reflexive
d_reflexive_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_142 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_142 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsPreMetric_96
v12
  = T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_142 T_IsPreMetric_96
v12
du_reflexive_142 ::
  T_IsPreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_142 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_142 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v1)) AgdaAny
v2)
-- Function.Metric.Structures.IsPreMetric._.EqC.sym
d_sym_144 ::
  T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_144 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_144 T_IsPreMetric_96
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))
-- Function.Metric.Structures.IsPreMetric._.EqC.trans
d_trans_146 ::
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_146 :: T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_146 T_IsPreMetric_96
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))
-- Function.Metric.Structures.IsPreMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_150 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_150 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_96
v12
  = T_IsPreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_150 T_IsPreMetric_96
v12
du_isPartialEquivalence_150 ::
  T_IsPreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_150 :: T_IsPreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_150 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.refl
d_refl_152 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny
d_refl_152 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny
d_refl_152 T_IsPreMetric_96
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.reflexive
d_reflexive_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_154 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_96
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_154 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsPreMetric_96
v12
  = T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_154 T_IsPreMetric_96
v12
du_reflexive_154 ::
  T_IsPreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_154 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_154 T_IsPreMetric_96
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Function.Metric.Structures.IsPreMetric._.Eq.sym
d_sym_156 ::
  T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_156 :: T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_156 T_IsPreMetric_96
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.trans
d_trans_158 ::
  T_IsPreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_158 :: T_IsPreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_158 T_IsPreMetric_96
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric
d_IsQuasiSemiMetric_162 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsQuasiSemiMetric_162 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 p
a11 = ()
data T_IsQuasiSemiMetric_162
  = C_IsQuasiSemiMetric'46'constructor_9549 T_IsPreMetric_96
                                            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsQuasiSemiMetric.isPreMetric
d_isPreMetric_170 :: T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 :: T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 T_IsQuasiSemiMetric_162
v0
  = case T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0 of
      C_IsQuasiSemiMetric'46'constructor_9549 T_IsPreMetric_96
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1
      T_IsQuasiSemiMetric_162
_ -> T_IsPreMetric_96
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsQuasiSemiMetric.0⇒≈
d_0'8658''8776'_172 ::
  T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_172 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_172 T_IsQuasiSemiMetric_162
v0
  = case T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0 of
      C_IsQuasiSemiMetric'46'constructor_9549 T_IsPreMetric_96
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_IsQuasiSemiMetric_162
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsQuasiSemiMetric._.antisym
d_antisym_176 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_176 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_176 T_IsQuasiSemiMetric_162
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.cong
d_cong_178 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_178 :: T_IsQuasiSemiMetric_162
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_178 T_IsQuasiSemiMetric_162
v0
  = (T_IsProtoMetric_30
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_46
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isEquivalence
d_isEquivalence_180 ::
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_180 :: T_IsQuasiSemiMetric_162 -> T_IsEquivalence_26
d_isEquivalence_180 T_IsQuasiSemiMetric_162
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isPartialOrder
d_isPartialOrder_182 ::
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_182 :: T_IsQuasiSemiMetric_162 -> T_IsPartialOrder_162
d_isPartialOrder_182 T_IsQuasiSemiMetric_162
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isPreorder
d_isPreorder_184 ::
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_184 :: T_IsQuasiSemiMetric_162 -> T_IsPreorder_70
d_isPreorder_184 T_IsQuasiSemiMetric_162
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isProtoMetric
d_isProtoMetric_186 ::
  T_IsQuasiSemiMetric_162 -> T_IsProtoMetric_30
d_isProtoMetric_186 :: T_IsQuasiSemiMetric_162 -> T_IsProtoMetric_30
d_isProtoMetric_186 T_IsQuasiSemiMetric_162
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))
-- Function.Metric.Structures.IsQuasiSemiMetric._.nonNegative
d_nonNegative_188 ::
  T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_188 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_188 T_IsQuasiSemiMetric_162
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.refl
d_refl_190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
d_refl_190 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> AgdaAny
-> AgdaAny
d_refl_190 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
du_refl_190 T_IsQuasiSemiMetric_162
v12
du_refl_190 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
du_refl_190 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
du_refl_190 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.reflexive
d_reflexive_192 ::
  T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_192 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_192 T_IsQuasiSemiMetric_162
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.trans
d_trans_194 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_194 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_194 T_IsQuasiSemiMetric_162
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_196 ::
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_196 :: T_IsQuasiSemiMetric_162 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_196 T_IsQuasiSemiMetric_162
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≈⇒0
d_'8776''8658'0_198 ::
  T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_198 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_198 T_IsQuasiSemiMetric_162
v0
  = (T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_106 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_200 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> T_Σ_14
d_'8764''45'resp'45''8776'_200 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162 -> T_Σ_14
du_'8764''45'resp'45''8776'_200 T_IsQuasiSemiMetric_162
v12
du_'8764''45'resp'45''8776'_200 ::
  T_IsQuasiSemiMetric_162 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_200 :: T_IsQuasiSemiMetric_162 -> T_Σ_14
du_'8764''45'resp'45''8776'_200 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_202 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_202 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_202 T_IsQuasiSemiMetric_162
v12
du_'8764''45'resp'691''45''8776'_202 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_202 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_202 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_204 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_204 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_204 T_IsQuasiSemiMetric_162
v12
du_'8764''45'resp'737''45''8776'_204 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_204 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_204 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_208 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_208 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_208 T_IsQuasiSemiMetric_162
v12
du_isPartialEquivalence_208 ::
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_208 :: T_IsQuasiSemiMetric_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_208 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v2))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.refl
d_refl_210 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
d_refl_210 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
d_refl_210 T_IsQuasiSemiMetric_162
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.reflexive
d_reflexive_212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_212 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_212 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_212 T_IsQuasiSemiMetric_162
v12
du_reflexive_212 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_212 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_212 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v2)) AgdaAny
v3))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.sym
d_sym_214 ::
  T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_214 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_214 T_IsQuasiSemiMetric_162
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.trans
d_trans_216 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_216 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_216 T_IsQuasiSemiMetric_162
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_220 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_220 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_220 T_IsQuasiSemiMetric_162
v12
du_isPartialEquivalence_220 ::
  T_IsQuasiSemiMetric_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_220 :: T_IsQuasiSemiMetric_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_220 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.refl
d_refl_222 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
d_refl_222 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny
d_refl_222 T_IsQuasiSemiMetric_162
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.reflexive
d_reflexive_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_224 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_162
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_224 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsQuasiSemiMetric_162
v12
  = T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_224 T_IsQuasiSemiMetric_162
v12
du_reflexive_224 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_224 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_224 T_IsQuasiSemiMetric_162
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))
                    AgdaAny
v5))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.sym
d_sym_226 ::
  T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_226 :: T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_226 T_IsQuasiSemiMetric_162
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.trans
d_trans_228 ::
  T_IsQuasiSemiMetric_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_228 :: T_IsQuasiSemiMetric_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_228 T_IsQuasiSemiMetric_162
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v0))))))
-- Function.Metric.Structures.IsSemiMetric
d_IsSemiMetric_232 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsSemiMetric_232 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 p
a11 = ()
data T_IsSemiMetric_232
  = C_IsSemiMetric'46'constructor_13167 T_IsQuasiSemiMetric_162
                                        (AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsSemiMetric.isQuasiSemiMetric
d_isQuasiSemiMetric_240 ::
  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 :: T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 T_IsSemiMetric_232
v0
  = case T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0 of
      C_IsSemiMetric'46'constructor_13167 T_IsQuasiSemiMetric_162
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1
      T_IsSemiMetric_232
_ -> T_IsQuasiSemiMetric_162
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsSemiMetric.sym
d_sym_242 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_242 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_242 T_IsSemiMetric_232
v0
  = case T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0 of
      C_IsSemiMetric'46'constructor_13167 T_IsQuasiSemiMetric_162
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemiMetric_232
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsSemiMetric._.0⇒≈
d_0'8658''8776'_246 ::
  T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_246 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_246 T_IsSemiMetric_232
v0
  = (T_IsQuasiSemiMetric_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_172 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))
-- Function.Metric.Structures.IsSemiMetric._.antisym
d_antisym_248 ::
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_248 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_248 T_IsSemiMetric_232
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.cong
d_cong_250 ::
  T_IsSemiMetric_232 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_250 :: T_IsSemiMetric_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_250 T_IsSemiMetric_232
v0
  = (T_IsProtoMetric_30
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_46
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))))
-- Function.Metric.Structures.IsSemiMetric._.isEquivalence
d_isEquivalence_252 ::
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_252 :: T_IsSemiMetric_232 -> T_IsEquivalence_26
d_isEquivalence_252 T_IsSemiMetric_232
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.isPartialOrder
d_isPartialOrder_254 ::
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_254 :: T_IsSemiMetric_232 -> T_IsPartialOrder_162
d_isPartialOrder_254 T_IsSemiMetric_232
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))))
-- Function.Metric.Structures.IsSemiMetric._.isPreMetric
d_isPreMetric_256 :: T_IsSemiMetric_232 -> T_IsPreMetric_96
d_isPreMetric_256 :: T_IsSemiMetric_232 -> T_IsPreMetric_96
d_isPreMetric_256 T_IsSemiMetric_232
v0
  = (T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96)
-> AgdaAny -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))
-- Function.Metric.Structures.IsSemiMetric._.isPreorder
d_isPreorder_258 ::
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_258 :: T_IsSemiMetric_232 -> T_IsPreorder_70
d_isPreorder_258 T_IsSemiMetric_232
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.isProtoMetric
d_isProtoMetric_260 :: T_IsSemiMetric_232 -> T_IsProtoMetric_30
d_isProtoMetric_260 :: T_IsSemiMetric_232 -> T_IsProtoMetric_30
d_isProtoMetric_260 T_IsSemiMetric_232
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))
-- Function.Metric.Structures.IsSemiMetric._.nonNegative
d_nonNegative_262 ::
  T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_262 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_262 T_IsSemiMetric_232
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))))
-- Function.Metric.Structures.IsSemiMetric._.refl
d_refl_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.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
d_refl_264 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> AgdaAny
-> AgdaAny
d_refl_264 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
du_refl_264 T_IsSemiMetric_232
v12
du_refl_264 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
du_refl_264 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
du_refl_264 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.reflexive
d_reflexive_266 ::
  T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_266 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_266 T_IsSemiMetric_232
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.trans
d_trans_268 ::
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_268 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_268 T_IsSemiMetric_232
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_270 ::
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_270 :: T_IsSemiMetric_232 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_270 T_IsSemiMetric_232
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0))))
-- Function.Metric.Structures.IsSemiMetric._.≈⇒0
d_'8776''8658'0_272 ::
  T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_272 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_272 T_IsSemiMetric_232
v0
  = (T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_106
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))
-- Function.Metric.Structures.IsSemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_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.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_274 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> T_Σ_14
d_'8764''45'resp'45''8776'_274 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232 -> T_Σ_14
du_'8764''45'resp'45''8776'_274 T_IsSemiMetric_232
v12
du_'8764''45'resp'45''8776'_274 ::
  T_IsSemiMetric_232 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_274 :: T_IsSemiMetric_232 -> T_Σ_14
du_'8764''45'resp'45''8776'_274 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_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.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_276 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_276 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_276 T_IsSemiMetric_232
v12
du_'8764''45'resp'691''45''8776'_276 ::
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_276 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_276 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_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.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_278 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_278 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_278 T_IsSemiMetric_232
v12
du_'8764''45'resp'737''45''8776'_278 ::
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_278 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_278 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_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.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_282 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_282 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_282 T_IsSemiMetric_232
v12
du_isPartialEquivalence_282 ::
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_282 :: T_IsSemiMetric_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_282 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v3)))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.refl
d_refl_284 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
d_refl_284 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
d_refl_284 T_IsSemiMetric_232
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.reflexive
d_reflexive_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.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_286 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_286 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_286 T_IsSemiMetric_232
v12
du_reflexive_286 ::
  T_IsSemiMetric_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_286 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_286 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v3)) AgdaAny
v4)))
-- Function.Metric.Structures.IsSemiMetric._.EqC.sym
d_sym_288 ::
  T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_288 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_288 T_IsSemiMetric_232
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.trans
d_trans_290 ::
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_290 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_290 T_IsSemiMetric_232
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_294 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_294 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_294 T_IsSemiMetric_232
v12
du_isPartialEquivalence_294 ::
  T_IsSemiMetric_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_294 :: T_IsSemiMetric_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_294 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                          (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.refl
d_refl_296 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
d_refl_296 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny
d_refl_296 T_IsSemiMetric_232
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
                  ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.reflexive
d_reflexive_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_298 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_232
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_298 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsSemiMetric_232
v12
  = T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_298 T_IsSemiMetric_232
v12
du_reflexive_298 ::
  T_IsSemiMetric_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_298 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_298 T_IsSemiMetric_232
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                          (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                          (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5))
                       AgdaAny
v6)))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.sym
d_sym_300 ::
  T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_300 :: T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_300 T_IsSemiMetric_232
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
                  ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.trans
d_trans_302 ::
  T_IsSemiMetric_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_302 :: T_IsSemiMetric_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_302 T_IsSemiMetric_232
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
                  ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric
d_IsGeneralMetric_308 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsGeneralMetric_308 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 p
a11 p
a12
  = ()
data T_IsGeneralMetric_308
  = C_IsGeneralMetric'46'constructor_17141 T_IsSemiMetric_232
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsGeneralMetric.isSemiMetric
d_isSemiMetric_318 :: T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 :: T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 T_IsGeneralMetric_308
v0
  = case T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0 of
      C_IsGeneralMetric'46'constructor_17141 T_IsSemiMetric_232
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1
      T_IsGeneralMetric_308
_ -> T_IsSemiMetric_232
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsGeneralMetric.triangle
d_triangle_320 ::
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_triangle_320 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_triangle_320 T_IsGeneralMetric_308
v0
  = case T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0 of
      C_IsGeneralMetric'46'constructor_17141 T_IsSemiMetric_232
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_IsGeneralMetric_308
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsGeneralMetric._.0⇒≈
d_0'8658''8776'_324 ::
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_324 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_324 T_IsGeneralMetric_308
v0
  = (T_IsQuasiSemiMetric_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_172
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))
-- Function.Metric.Structures.IsGeneralMetric._.antisym
d_antisym_326 ::
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_326 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_326 T_IsGeneralMetric_308
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.cong
d_cong_328 ::
  T_IsGeneralMetric_308 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_328 :: T_IsGeneralMetric_308
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_328 T_IsGeneralMetric_308
v0
  = (T_IsProtoMetric_30
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_46
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.isEquivalence
d_isEquivalence_330 ::
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_330 :: T_IsGeneralMetric_308 -> T_IsEquivalence_26
d_isEquivalence_330 T_IsGeneralMetric_308
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.isPartialOrder
d_isPartialOrder_332 ::
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_332 :: T_IsGeneralMetric_308 -> T_IsPartialOrder_162
d_isPartialOrder_332 T_IsGeneralMetric_308
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.isPreMetric
d_isPreMetric_334 :: T_IsGeneralMetric_308 -> T_IsPreMetric_96
d_isPreMetric_334 :: T_IsGeneralMetric_308 -> T_IsPreMetric_96
d_isPreMetric_334 T_IsGeneralMetric_308
v0
  = (T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96)
-> AgdaAny -> T_IsPreMetric_96
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))
-- Function.Metric.Structures.IsGeneralMetric._.isPreorder
d_isPreorder_336 ::
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_336 :: T_IsGeneralMetric_308 -> T_IsPreorder_70
d_isPreorder_336 T_IsGeneralMetric_308
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.isProtoMetric
d_isProtoMetric_338 :: T_IsGeneralMetric_308 -> T_IsProtoMetric_30
d_isProtoMetric_338 :: T_IsGeneralMetric_308 -> T_IsProtoMetric_30
d_isProtoMetric_338 T_IsGeneralMetric_308
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
         ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))
-- Function.Metric.Structures.IsGeneralMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_340 ::
  T_IsGeneralMetric_308 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_340 :: T_IsGeneralMetric_308 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_340 T_IsGeneralMetric_308
v0
  = (T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))
-- Function.Metric.Structures.IsGeneralMetric._.nonNegative
d_nonNegative_342 ::
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_342 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_342 T_IsGeneralMetric_308
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.refl
d_refl_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.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
d_refl_344 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> AgdaAny
-> AgdaAny
d_refl_344 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 ~AgdaAny -> AgdaAny -> AgdaAny
v12
           T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
du_refl_344 T_IsGeneralMetric_308
v13
du_refl_344 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
du_refl_344 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
du_refl_344 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.reflexive
d_reflexive_346 ::
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_346 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_346 T_IsGeneralMetric_308
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.sym
d_sym_348 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_348 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_348 T_IsGeneralMetric_308
v0 = (T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_242 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))
-- Function.Metric.Structures.IsGeneralMetric._.trans
d_trans_350 ::
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_350 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_350 T_IsGeneralMetric_308
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_352 ::
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_352 :: T_IsGeneralMetric_308 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_352 T_IsGeneralMetric_308
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.≈⇒0
d_'8776''8658'0_354 ::
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_354 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_354 T_IsGeneralMetric_308
v0
  = (T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_106
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
         ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_356 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> T_Σ_14
d_'8764''45'resp'45''8776'_356 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 ~AgdaAny -> AgdaAny -> AgdaAny
v12 T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308 -> T_Σ_14
du_'8764''45'resp'45''8776'_356 T_IsGeneralMetric_308
v13
du_'8764''45'resp'45''8776'_356 ::
  T_IsGeneralMetric_308 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_356 :: T_IsGeneralMetric_308 -> T_Σ_14
du_'8764''45'resp'45''8776'_356 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_358 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_358 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 ~AgdaAny -> AgdaAny -> AgdaAny
v12 T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_358 T_IsGeneralMetric_308
v13
du_'8764''45'resp'691''45''8776'_358 ::
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_358 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_358 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_360 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_360 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 ~AgdaAny -> AgdaAny -> AgdaAny
v12 T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_360 T_IsGeneralMetric_308
v13
du_'8764''45'resp'737''45''8776'_360 ::
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_360 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_360 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_364 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_364 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 ~AgdaAny -> AgdaAny -> AgdaAny
v12 T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_364 T_IsGeneralMetric_308
v13
du_isPartialEquivalence_364 ::
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_364 :: T_IsGeneralMetric_308 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_364 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v4))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.refl
d_refl_366 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
d_refl_366 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
d_refl_366 T_IsGeneralMetric_308
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.reflexive
d_reflexive_368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_368 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_368 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                ~AgdaAny -> AgdaAny -> AgdaAny
v12 T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_368 T_IsGeneralMetric_308
v13
du_reflexive_368 ::
  T_IsGeneralMetric_308 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_368 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_368 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v4)) AgdaAny
v5))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.sym
d_sym_370 ::
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_370 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_370 T_IsGeneralMetric_308
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.trans
d_trans_372 ::
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_372 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_372 T_IsGeneralMetric_308
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_376 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_376 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 ~AgdaAny -> AgdaAny -> AgdaAny
v12 T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_IsGeneralMetric_308
v13
du_isPartialEquivalence_376 ::
  T_IsGeneralMetric_308 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_376 :: T_IsGeneralMetric_308 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPreorder_70
v6
                         = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                             (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.refl
d_refl_378 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
d_refl_378 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny
d_refl_378 T_IsGeneralMetric_308
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
                  ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
                     ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.reflexive
d_reflexive_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_308 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_380 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_308
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_380 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                ~AgdaAny -> AgdaAny -> AgdaAny
v12 T_IsGeneralMetric_308
v13
  = T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_380 T_IsGeneralMetric_308
v13
du_reflexive_380 ::
  T_IsGeneralMetric_308 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_380 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_380 T_IsGeneralMetric_308
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2 = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3 = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42 (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPreorder_70
v6
                         = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                             (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                             (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))
                          AgdaAny
v7))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.sym
d_sym_382 ::
  T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_382 :: T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_382 T_IsGeneralMetric_308
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
                  ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
                     ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.trans
d_trans_384 ::
  T_IsGeneralMetric_308 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_384 :: T_IsGeneralMetric_308
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_384 T_IsGeneralMetric_308
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_162
d_isPartialOrder_42
               ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_104
                  ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
d_isPreMetric_170
                     ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_240 ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308 -> T_IsSemiMetric_232
d_isSemiMetric_318 (T_IsGeneralMetric_308 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_308
v0))))))))