{-# 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_174
                                        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_174
d_isPartialOrder_42 :: T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174
v1 T_IsEquivalence_26
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v1
      T_IsProtoMetric_30
_ -> T_IsPartialOrder_174
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_174
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_174
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_174
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_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
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_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
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_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Function.Metric.Structures.IsProtoMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_70 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.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_'8818''45'resp'45''8776'_70 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> T_Σ_14
d_'8818''45'resp'45''8776'_70 ~()
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_'8818''45'resp'45''8776'_70 T_IsProtoMetric_30
v12
du_'8818''45'resp'45''8776'_70 ::
  T_IsProtoMetric_30 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_70 :: T_IsProtoMetric_30 -> T_Σ_14
du_'8818''45'resp'45''8776'_70 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Function.Metric.Structures.IsProtoMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_72 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_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
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_72 T_IsProtoMetric_30
v12
du_'8818''45'resp'691''45''8776'_72 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_72 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_72 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Function.Metric.Structures.IsProtoMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_74 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_'8818''45'resp'737''45''8776'_74 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_74 ~()
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_'8818''45'resp'737''45''8776'_74 T_IsProtoMetric_30
v12
du_'8818''45'resp'737''45''8776'_74 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_74 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_74 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Function.Metric.Structures.IsProtoMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_78 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_78 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_78 ~()
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_78 T_IsProtoMetric_30
v12
du_isPartialEquivalence_78 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_78 :: T_IsProtoMetric_30 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_78 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_80 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_80 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_80 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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.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_82 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_82 ~()
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_82 T_IsProtoMetric_30
v12
du_reflexive_82 ::
  T_IsProtoMetric_30 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_82 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_82 T_IsProtoMetric_30
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_84 ::
  T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_84 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_84 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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_86 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_86 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_86 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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_90 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.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_90 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_90 ~()
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_90 T_IsProtoMetric_30
v12
du_isPartialEquivalence_90 ::
  T_IsProtoMetric_30 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_90 :: T_IsProtoMetric_30 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_90 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_92 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_92 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny
d_refl_92 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_94 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_94 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsProtoMetric_30
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_94 ~()
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_94 T_IsProtoMetric_30
v12
du_reflexive_94 ::
  T_IsProtoMetric_30 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_94 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_94 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_96 ::
  T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_96 :: T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_96 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_98 ::
  T_IsProtoMetric_30 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_98 :: T_IsProtoMetric_30
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_98 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_102 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsPreMetric_102 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_102
  = C_IsPreMetric'46'constructor_6347 T_IsProtoMetric_30
                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsPreMetric.isProtoMetric
d_isProtoMetric_110 :: T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 :: T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 T_IsPreMetric_102
v0
  = case T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0 of
      C_IsPreMetric'46'constructor_6347 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_102
_ -> T_IsProtoMetric_30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsPreMetric.≈⇒0
d_'8776''8658'0_112 ::
  T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_112 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_112 T_IsPreMetric_102
v0
  = case T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0 of
      C_IsPreMetric'46'constructor_6347 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_102
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsPreMetric._.antisym
d_antisym_116 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_116 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_116 T_IsPreMetric_102
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))
-- Function.Metric.Structures.IsPreMetric._.cong
d_cong_118 ::
  T_IsPreMetric_102 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_118 :: T_IsPreMetric_102
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_118 T_IsPreMetric_102
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0))
-- Function.Metric.Structures.IsPreMetric._.isEquivalence
d_isEquivalence_120 ::
  T_IsPreMetric_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_120 :: T_IsPreMetric_102 -> T_IsEquivalence_26
d_isEquivalence_120 T_IsPreMetric_102
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0))))
-- Function.Metric.Structures.IsPreMetric._.isPartialOrder
d_isPartialOrder_122 ::
  T_IsPreMetric_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_122 :: T_IsPreMetric_102 -> T_IsPartialOrder_174
d_isPartialOrder_122 T_IsPreMetric_102
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0))
-- Function.Metric.Structures.IsPreMetric._.isPreorder
d_isPreorder_124 ::
  T_IsPreMetric_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_124 :: T_IsPreMetric_102 -> T_IsPreorder_70
d_isPreorder_124 T_IsPreMetric_102
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))
-- Function.Metric.Structures.IsPreMetric._.nonNegative
d_nonNegative_126 ::
  T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_126 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_126 T_IsPreMetric_102
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0))
-- Function.Metric.Structures.IsPreMetric._.refl
d_refl_128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_102 -> AgdaAny -> AgdaAny
d_refl_128 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> AgdaAny
-> AgdaAny
d_refl_128 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_102
v12
  = T_IsPreMetric_102 -> AgdaAny -> AgdaAny
du_refl_128 T_IsPreMetric_102
v12
du_refl_128 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny
du_refl_128 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny
du_refl_128 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Structures.IsPreMetric._.reflexive
d_reflexive_130 ::
  T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_130 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_130 T_IsPreMetric_102
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0))))
-- Function.Metric.Structures.IsPreMetric._.trans
d_trans_132 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_132 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_132 T_IsPreMetric_102
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0))))
-- Function.Metric.Structures.IsPreMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_134 ::
  T_IsPreMetric_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_134 :: T_IsPreMetric_102 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_134 T_IsPreMetric_102
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0))
-- Function.Metric.Structures.IsPreMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_102 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_136 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> T_Σ_14
d_'8764''45'resp'45''8776'_136 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_102
v12
  = T_IsPreMetric_102 -> T_Σ_14
du_'8764''45'resp'45''8776'_136 T_IsPreMetric_102
v12
du_'8764''45'resp'45''8776'_136 ::
  T_IsPreMetric_102 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_136 :: T_IsPreMetric_102 -> T_Σ_14
du_'8764''45'resp'45''8776'_136 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Structures.IsPreMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_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_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_138 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_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_102
v12
  = T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_138 T_IsPreMetric_102
v12
du_'8764''45'resp'691''45''8776'_138 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_138 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_138 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Structures.IsPreMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_140 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_140 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_102
v12
  = T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_140 T_IsPreMetric_102
v12
du_'8764''45'resp'737''45''8776'_140 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_140 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_140 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Structures.IsPreMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_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_102 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_142 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> T_Σ_14
d_'8818''45'resp'45''8776'_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_102
v12
  = T_IsPreMetric_102 -> T_Σ_14
du_'8818''45'resp'45''8776'_142 T_IsPreMetric_102
v12
du_'8818''45'resp'45''8776'_142 ::
  T_IsPreMetric_102 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_142 :: T_IsPreMetric_102 -> T_Σ_14
du_'8818''45'resp'45''8776'_142 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Structures.IsPreMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_144 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_144 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_102
v12
  = T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_144 T_IsPreMetric_102
v12
du_'8818''45'resp'691''45''8776'_144 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_144 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_144 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Structures.IsPreMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_146 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_146 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_102
v12
  = T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_146 T_IsPreMetric_102
v12
du_'8818''45'resp'737''45''8776'_146 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_146 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_146 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Structures.IsPreMetric._.EqC.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_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_150 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> 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_102
v12
  = T_IsPreMetric_102 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_150 T_IsPreMetric_102
v12
du_isPartialEquivalence_150 ::
  T_IsPreMetric_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_150 :: T_IsPreMetric_102 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_150 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_152 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny
d_refl_152 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny
d_refl_152 T_IsPreMetric_102
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))
-- Function.Metric.Structures.IsPreMetric._.EqC.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_102 ->
  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_102
-> 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_102
v12
  = T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_154 T_IsPreMetric_102
v12
du_reflexive_154 ::
  T_IsPreMetric_102 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_154 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_154 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_156 ::
  T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_156 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_156 T_IsPreMetric_102
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))
-- Function.Metric.Structures.IsPreMetric._.EqC.trans
d_trans_158 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_158 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_158 T_IsPreMetric_102
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))
-- Function.Metric.Structures.IsPreMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_162 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_162 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_102
v12
  = T_IsPreMetric_102 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_162 T_IsPreMetric_102
v12
du_isPartialEquivalence_162 ::
  T_IsPreMetric_102 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_162 :: T_IsPreMetric_102 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_162 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_164 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny
d_refl_164 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny
d_refl_164 T_IsPreMetric_102
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.reflexive
d_reflexive_166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_102 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_166 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_102
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_166 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsPreMetric_102
v12
  = T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_166 T_IsPreMetric_102
v12
du_reflexive_166 ::
  T_IsPreMetric_102 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_166 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_166 T_IsPreMetric_102
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_168 ::
  T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 :: T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 T_IsPreMetric_102
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.trans
d_trans_170 ::
  T_IsPreMetric_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 :: T_IsPreMetric_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 T_IsPreMetric_102
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42 ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric
d_IsQuasiSemiMetric_174 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsQuasiSemiMetric_174 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_174
  = C_IsQuasiSemiMetric'46'constructor_10111 T_IsPreMetric_102
                                             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsQuasiSemiMetric.isPreMetric
d_isPreMetric_182 :: T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 :: T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 T_IsQuasiSemiMetric_174
v0
  = case T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0 of
      C_IsQuasiSemiMetric'46'constructor_10111 T_IsPreMetric_102
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1
      T_IsQuasiSemiMetric_174
_ -> T_IsPreMetric_102
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsQuasiSemiMetric.0⇒≈
d_0'8658''8776'_184 ::
  T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_184 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_184 T_IsQuasiSemiMetric_174
v0
  = case T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0 of
      C_IsQuasiSemiMetric'46'constructor_10111 T_IsPreMetric_102
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_174
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsQuasiSemiMetric._.antisym
d_antisym_188 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_188 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_188 T_IsQuasiSemiMetric_174
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.cong
d_cong_190 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_190 :: T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_190 T_IsQuasiSemiMetric_174
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isEquivalence
d_isEquivalence_192 ::
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_192 :: T_IsQuasiSemiMetric_174 -> T_IsEquivalence_26
d_isEquivalence_192 T_IsQuasiSemiMetric_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isPartialOrder
d_isPartialOrder_194 ::
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_194 :: T_IsQuasiSemiMetric_174 -> T_IsPartialOrder_174
d_isPartialOrder_194 T_IsQuasiSemiMetric_174
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isPreorder
d_isPreorder_196 ::
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_196 :: T_IsQuasiSemiMetric_174 -> T_IsPreorder_70
d_isPreorder_196 T_IsQuasiSemiMetric_174
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isProtoMetric
d_isProtoMetric_198 ::
  T_IsQuasiSemiMetric_174 -> T_IsProtoMetric_30
d_isProtoMetric_198 :: T_IsQuasiSemiMetric_174 -> T_IsProtoMetric_30
d_isProtoMetric_198 T_IsQuasiSemiMetric_174
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))
-- Function.Metric.Structures.IsQuasiSemiMetric._.nonNegative
d_nonNegative_200 ::
  T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_200 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_200 T_IsQuasiSemiMetric_174
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.refl
d_refl_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_174 -> AgdaAny -> AgdaAny
d_refl_202 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
d_refl_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_174
v12
  = T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny
du_refl_202 T_IsQuasiSemiMetric_174
v12
du_refl_202 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny
du_refl_202 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny
du_refl_202 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.reflexive
d_reflexive_204 ::
  T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_204 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_204 T_IsQuasiSemiMetric_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.trans
d_trans_206 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_206 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_206 T_IsQuasiSemiMetric_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_208 ::
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_208 :: T_IsQuasiSemiMetric_174 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_208 T_IsQuasiSemiMetric_174
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≈⇒0
d_'8776''8658'0_210 ::
  T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_210 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_210 T_IsQuasiSemiMetric_174
v0
  = (T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_112 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_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_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_212 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> T_Σ_14
d_'8764''45'resp'45''8776'_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_174
v12
  = T_IsQuasiSemiMetric_174 -> T_Σ_14
du_'8764''45'resp'45''8776'_212 T_IsQuasiSemiMetric_174
v12
du_'8764''45'resp'45''8776'_212 ::
  T_IsQuasiSemiMetric_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_212 :: T_IsQuasiSemiMetric_174 -> T_Σ_14
du_'8764''45'resp'45''8776'_212 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_214 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_214 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_214 T_IsQuasiSemiMetric_174
v12
du_'8764''45'resp'691''45''8776'_214 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_214 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_214 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_216 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_216 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_216 T_IsQuasiSemiMetric_174
v12
du_'8764''45'resp'737''45''8776'_216 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_216 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_216 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_218 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> T_Σ_14
d_'8818''45'resp'45''8776'_218 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174 -> T_Σ_14
du_'8818''45'resp'45''8776'_218 T_IsQuasiSemiMetric_174
v12
du_'8818''45'resp'45''8776'_218 ::
  T_IsQuasiSemiMetric_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_218 :: T_IsQuasiSemiMetric_174 -> T_Σ_14
du_'8818''45'resp'45''8776'_218 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_220 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_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_174
v12
  = T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_220 T_IsQuasiSemiMetric_174
v12
du_'8818''45'resp'691''45''8776'_220 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_220 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_220 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_222 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_222 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_222 T_IsQuasiSemiMetric_174
v12
du_'8818''45'resp'737''45''8776'_222 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_222 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_222 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_226 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_226 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_226 T_IsQuasiSemiMetric_174
v12
du_isPartialEquivalence_226 ::
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_226 :: T_IsQuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_226 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_228 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny
d_refl_228 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny
d_refl_228 T_IsQuasiSemiMetric_174
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.reflexive
d_reflexive_230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_230 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_230 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_230 T_IsQuasiSemiMetric_174
v12
du_reflexive_230 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_230 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_230 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_232 ::
  T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_232 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_232 T_IsQuasiSemiMetric_174
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.trans
d_trans_234 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_234 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_234 T_IsQuasiSemiMetric_174
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_238 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_238 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_238 T_IsQuasiSemiMetric_174
v12
du_isPartialEquivalence_238 ::
  T_IsQuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_238 :: T_IsQuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_238 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                       (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_240 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny
d_refl_240 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny
d_refl_240 T_IsQuasiSemiMetric_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.reflexive
d_reflexive_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_242 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_242 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsQuasiSemiMetric_174
v12
  = T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_242 T_IsQuasiSemiMetric_174
v12
du_reflexive_242 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_242 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_242 T_IsQuasiSemiMetric_174
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                       (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_244 ::
  T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_244 :: T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_244 T_IsQuasiSemiMetric_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.trans
d_trans_246 ::
  T_IsQuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_246 :: T_IsQuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_246 T_IsQuasiSemiMetric_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v0))))))
-- Function.Metric.Structures.IsSemiMetric
d_IsSemiMetric_250 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsSemiMetric_250 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_250
  = C_IsSemiMetric'46'constructor_14005 T_IsQuasiSemiMetric_174
                                        (AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsSemiMetric.isQuasiSemiMetric
d_isQuasiSemiMetric_258 ::
  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 :: T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 T_IsSemiMetric_250
v0
  = case T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0 of
      C_IsSemiMetric'46'constructor_14005 T_IsQuasiSemiMetric_174
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1
      T_IsSemiMetric_250
_ -> T_IsQuasiSemiMetric_174
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsSemiMetric.sym
d_sym_260 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_260 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_260 T_IsSemiMetric_250
v0
  = case T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0 of
      C_IsSemiMetric'46'constructor_14005 T_IsQuasiSemiMetric_174
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemiMetric_250
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsSemiMetric._.0⇒≈
d_0'8658''8776'_264 ::
  T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_264 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_264 T_IsSemiMetric_250
v0
  = (T_IsQuasiSemiMetric_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_184 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))
-- Function.Metric.Structures.IsSemiMetric._.antisym
d_antisym_266 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_266 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_266 T_IsSemiMetric_250
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.cong
d_cong_268 ::
  T_IsSemiMetric_250 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_268 :: T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_268 T_IsSemiMetric_250
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))))
-- Function.Metric.Structures.IsSemiMetric._.isEquivalence
d_isEquivalence_270 ::
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_270 :: T_IsSemiMetric_250 -> T_IsEquivalence_26
d_isEquivalence_270 T_IsSemiMetric_250
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.isPartialOrder
d_isPartialOrder_272 ::
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_272 :: T_IsSemiMetric_250 -> T_IsPartialOrder_174
d_isPartialOrder_272 T_IsSemiMetric_250
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))))
-- Function.Metric.Structures.IsSemiMetric._.isPreMetric
d_isPreMetric_274 :: T_IsSemiMetric_250 -> T_IsPreMetric_102
d_isPreMetric_274 :: T_IsSemiMetric_250 -> T_IsPreMetric_102
d_isPreMetric_274 T_IsSemiMetric_250
v0
  = (T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))
-- Function.Metric.Structures.IsSemiMetric._.isPreorder
d_isPreorder_276 ::
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_276 :: T_IsSemiMetric_250 -> T_IsPreorder_70
d_isPreorder_276 T_IsSemiMetric_250
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.isProtoMetric
d_isProtoMetric_278 :: T_IsSemiMetric_250 -> T_IsProtoMetric_30
d_isProtoMetric_278 :: T_IsSemiMetric_250 -> T_IsProtoMetric_30
d_isProtoMetric_278 T_IsSemiMetric_250
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))
-- Function.Metric.Structures.IsSemiMetric._.nonNegative
d_nonNegative_280 ::
  T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_280 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_280 T_IsSemiMetric_250
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))))
-- Function.Metric.Structures.IsSemiMetric._.refl
d_refl_282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
d_refl_282 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
d_refl_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_250
v12
  = T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
du_refl_282 T_IsSemiMetric_250
v12
du_refl_282 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
du_refl_282 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
du_refl_282 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.reflexive
d_reflexive_284 ::
  T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_284 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_284 T_IsSemiMetric_250
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.trans
d_trans_286 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_286 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_286 T_IsSemiMetric_250
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_288 ::
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_288 :: T_IsSemiMetric_250 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_288 T_IsSemiMetric_250
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0))))
-- Function.Metric.Structures.IsSemiMetric._.≈⇒0
d_'8776''8658'0_290 ::
  T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_290 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_290 T_IsSemiMetric_250
v0
  = (T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_112
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))
-- Function.Metric.Structures.IsSemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_250 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_292 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> T_Σ_14
d_'8764''45'resp'45''8776'_292 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250 -> T_Σ_14
du_'8764''45'resp'45''8776'_292 T_IsSemiMetric_250
v12
du_'8764''45'resp'45''8776'_292 ::
  T_IsSemiMetric_250 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_292 :: T_IsSemiMetric_250 -> T_Σ_14
du_'8764''45'resp'45''8776'_292 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_294 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_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_250
v12
  = T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_294 T_IsSemiMetric_250
v12
du_'8764''45'resp'691''45''8776'_294 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_294 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_294 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_296 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_296 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_296 T_IsSemiMetric_250
v12
du_'8764''45'resp'737''45''8776'_296 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_296 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_296 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_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_250 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_298 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> T_Σ_14
d_'8818''45'resp'45''8776'_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_250
v12
  = T_IsSemiMetric_250 -> T_Σ_14
du_'8818''45'resp'45''8776'_298 T_IsSemiMetric_250
v12
du_'8818''45'resp'45''8776'_298 ::
  T_IsSemiMetric_250 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_298 :: T_IsSemiMetric_250 -> T_Σ_14
du_'8818''45'resp'45''8776'_298 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_300 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_300 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_300 T_IsSemiMetric_250
v12
du_'8818''45'resp'691''45''8776'_300 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_300 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_300 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_302 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_302 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_302 T_IsSemiMetric_250
v12
du_'8818''45'resp'737''45''8776'_302 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_302 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_302 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_306 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_306 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_306 T_IsSemiMetric_250
v12
du_isPartialEquivalence_306 ::
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_306 :: T_IsSemiMetric_250 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_306 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_308 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
d_refl_308 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
d_refl_308 T_IsSemiMetric_250
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.reflexive
d_reflexive_310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_310 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_310 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_310 T_IsSemiMetric_250
v12
du_reflexive_310 ::
  T_IsSemiMetric_250 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_310 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_310 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_312 ::
  T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_312 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_312 T_IsSemiMetric_250
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.trans
d_trans_314 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_314 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_314 T_IsSemiMetric_250
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_318 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_318 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_318 T_IsSemiMetric_250
v12
du_isPartialEquivalence_318 ::
  T_IsSemiMetric_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_318 :: T_IsSemiMetric_250 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_318 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                          (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_320 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
d_refl_320 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny
d_refl_320 T_IsSemiMetric_250
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
                  ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.reflexive
d_reflexive_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_250 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_322 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_250
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_322 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsSemiMetric_250
v12
  = T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_322 T_IsSemiMetric_250
v12
du_reflexive_322 ::
  T_IsSemiMetric_250 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_322 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_322 T_IsSemiMetric_250
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                          (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_324 ::
  T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_324 :: T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_324 T_IsSemiMetric_250
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
                  ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.trans
d_trans_326 ::
  T_IsSemiMetric_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_326 :: T_IsSemiMetric_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_326 T_IsSemiMetric_250
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
                  ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric
d_IsGeneralMetric_332 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsGeneralMetric_332 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_332
  = C_IsGeneralMetric'46'constructor_18255 T_IsSemiMetric_250
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsGeneralMetric.isSemiMetric
d_isSemiMetric_342 :: T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 :: T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 T_IsGeneralMetric_332
v0
  = case T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0 of
      C_IsGeneralMetric'46'constructor_18255 T_IsSemiMetric_250
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1
      T_IsGeneralMetric_332
_ -> T_IsSemiMetric_250
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsGeneralMetric.triangle
d_triangle_344 ::
  T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_triangle_344 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_triangle_344 T_IsGeneralMetric_332
v0
  = case T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0 of
      C_IsGeneralMetric'46'constructor_18255 T_IsSemiMetric_250
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_332
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsGeneralMetric._.0⇒≈
d_0'8658''8776'_348 ::
  T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_348 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_348 T_IsGeneralMetric_332
v0
  = (T_IsQuasiSemiMetric_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_184
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))
-- Function.Metric.Structures.IsGeneralMetric._.antisym
d_antisym_350 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_350 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_350 T_IsGeneralMetric_332
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.cong
d_cong_352 ::
  T_IsGeneralMetric_332 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_352 :: T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_352 T_IsGeneralMetric_332
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.isEquivalence
d_isEquivalence_354 ::
  T_IsGeneralMetric_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_354 :: T_IsGeneralMetric_332 -> T_IsEquivalence_26
d_isEquivalence_354 T_IsGeneralMetric_332
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.isPartialOrder
d_isPartialOrder_356 ::
  T_IsGeneralMetric_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_356 :: T_IsGeneralMetric_332 -> T_IsPartialOrder_174
d_isPartialOrder_356 T_IsGeneralMetric_332
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.isPreMetric
d_isPreMetric_358 :: T_IsGeneralMetric_332 -> T_IsPreMetric_102
d_isPreMetric_358 :: T_IsGeneralMetric_332 -> T_IsPreMetric_102
d_isPreMetric_358 T_IsGeneralMetric_332
v0
  = (T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> T_IsPreMetric_102
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))
-- Function.Metric.Structures.IsGeneralMetric._.isPreorder
d_isPreorder_360 ::
  T_IsGeneralMetric_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_360 :: T_IsGeneralMetric_332 -> T_IsPreorder_70
d_isPreorder_360 T_IsGeneralMetric_332
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.isProtoMetric
d_isProtoMetric_362 :: T_IsGeneralMetric_332 -> T_IsProtoMetric_30
d_isProtoMetric_362 :: T_IsGeneralMetric_332 -> T_IsProtoMetric_30
d_isProtoMetric_362 T_IsGeneralMetric_332
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
         ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))
-- Function.Metric.Structures.IsGeneralMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_364 ::
  T_IsGeneralMetric_332 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_364 :: T_IsGeneralMetric_332 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_364 T_IsGeneralMetric_332
v0
  = (T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))
-- Function.Metric.Structures.IsGeneralMetric._.nonNegative
d_nonNegative_366 ::
  T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_366 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_366 T_IsGeneralMetric_332
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.refl
d_refl_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_332 -> AgdaAny -> AgdaAny
d_refl_368 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
d_refl_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_332
v13
  = T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny
du_refl_368 T_IsGeneralMetric_332
v13
du_refl_368 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny
du_refl_368 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny
du_refl_368 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.reflexive
d_reflexive_370 ::
  T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_370 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_370 T_IsGeneralMetric_332
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.sym
d_sym_372 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_372 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_372 T_IsGeneralMetric_332
v0 = (T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_260 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))
-- Function.Metric.Structures.IsGeneralMetric._.trans
d_trans_374 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_374 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_374 T_IsGeneralMetric_332
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_376 ::
  T_IsGeneralMetric_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_376 :: T_IsGeneralMetric_332 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_376 T_IsGeneralMetric_332
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.≈⇒0
d_'8776''8658'0_378 ::
  T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_378 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_378 T_IsGeneralMetric_332
v0
  = (T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreMetric_102 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_112
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
         ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_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_332 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_380 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> T_Σ_14
d_'8764''45'resp'45''8776'_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_332
v13
  = T_IsGeneralMetric_332 -> T_Σ_14
du_'8764''45'resp'45''8776'_380 T_IsGeneralMetric_332
v13
du_'8764''45'resp'45''8776'_380 ::
  T_IsGeneralMetric_332 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_380 :: T_IsGeneralMetric_332 -> T_Σ_14
du_'8764''45'resp'45''8776'_380 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_382 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_382 ~()
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_332
v13
  = T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_382 T_IsGeneralMetric_332
v13
du_'8764''45'resp'691''45''8776'_382 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_382 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_382 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_384 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_384 ~()
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_332
v13
  = T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_384 T_IsGeneralMetric_332
v13
du_'8764''45'resp'737''45''8776'_384 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_384 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_384 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_386 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> T_Σ_14
d_'8818''45'resp'45''8776'_386 ~()
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_332
v13
  = T_IsGeneralMetric_332 -> T_Σ_14
du_'8818''45'resp'45''8776'_386 T_IsGeneralMetric_332
v13
du_'8818''45'resp'45''8776'_386 ::
  T_IsGeneralMetric_332 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_386 :: T_IsGeneralMetric_332 -> T_Σ_14
du_'8818''45'resp'45''8776'_386 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_388 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_388 ~()
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_332
v13
  = T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_388 T_IsGeneralMetric_332
v13
du_'8818''45'resp'691''45''8776'_388 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_388 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_388 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_390 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_390 ~()
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_332
v13
  = T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_390 T_IsGeneralMetric_332
v13
du_'8818''45'resp'737''45''8776'_390 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_390 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_390 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_394 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_394 ~()
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_332
v13
  = T_IsGeneralMetric_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_394 T_IsGeneralMetric_332
v13
du_isPartialEquivalence_394 ::
  T_IsGeneralMetric_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_394 :: T_IsGeneralMetric_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_394 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_396 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny
d_refl_396 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny
d_refl_396 T_IsGeneralMetric_332
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.reflexive
d_reflexive_398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_398 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_398 ~()
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_332
v13
  = T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_398 T_IsGeneralMetric_332
v13
du_reflexive_398 ::
  T_IsGeneralMetric_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_398 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_398 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_400 ::
  T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_400 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_400 T_IsGeneralMetric_332
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.trans
d_trans_402 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_402 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_402 T_IsGeneralMetric_332
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_406 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_406 ~()
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_332
v13
  = T_IsGeneralMetric_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_406 T_IsGeneralMetric_332
v13
du_isPartialEquivalence_406 ::
  T_IsGeneralMetric_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_406 :: T_IsGeneralMetric_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_406 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                             (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_408 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny
d_refl_408 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny
d_refl_408 T_IsGeneralMetric_332
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
                  ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
                     ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.reflexive
d_reflexive_410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_410 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_332
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_410 ~()
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_332
v13
  = T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_410 T_IsGeneralMetric_332
v13
du_reflexive_410 ::
  T_IsGeneralMetric_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_410 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_410 T_IsGeneralMetric_332
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2 = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3 = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                             (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_412 ::
  T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_412 :: T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_412 T_IsGeneralMetric_332
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
                  ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
                     ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.trans
d_trans_414 ::
  T_IsGeneralMetric_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_414 :: T_IsGeneralMetric_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_414 T_IsGeneralMetric_332
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_174
d_isPartialOrder_42
               ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_102 -> T_IsProtoMetric_30
d_isProtoMetric_110
                  ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
d_isPreMetric_182
                     ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_258 ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332 -> T_IsSemiMetric_250
d_isSemiMetric_342 (T_IsGeneralMetric_332 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_332
v0))))))))