{-# 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_constructor_100 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
                      MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
                      (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_248
d_isPartialOrder_42 :: T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_constructor_100 T_IsPartialOrder_248
v1 T_IsEquivalence_28
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1
      T_IsProtoMetric_30
_ -> T_IsPartialOrder_248
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_28
d_'8776''45'isEquivalence_44 :: T_IsProtoMetric_30 -> T_IsEquivalence_28
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_constructor_100 T_IsPartialOrder_248
v1 T_IsEquivalence_28
v2 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsEquivalence_28 -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsEquivalence_28
v2
      T_IsProtoMetric_30
_ -> T_IsEquivalence_28
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_constructor_100 T_IsPartialOrder_248
v1 T_IsEquivalence_28
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_constructor_100 T_IsPartialOrder_248
v1 T_IsEquivalence_28
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_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_28
d_isEquivalence_54 :: T_IsProtoMetric_30 -> T_IsEquivalence_28
d_isEquivalence_54 T_IsProtoMetric_30
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
d_isPreorder_56 :: T_IsProtoMetric_30 -> T_IsPreorder_76
d_isPreorder_56 T_IsProtoMetric_30
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
               (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_248
v1 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                 (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_104 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsPreMetric_104 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_104
  = C_constructor_174 T_IsProtoMetric_30
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsPreMetric.isProtoMetric
d_isProtoMetric_112 :: T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 :: T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 T_IsPreMetric_104
v0
  = case T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0 of
      C_constructor_174 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_104
_ -> T_IsProtoMetric_30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsPreMetric.≈⇒0
d_'8776''8658'0_114 ::
  T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_114 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_114 T_IsPreMetric_104
v0
  = case T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0 of
      C_constructor_174 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_104
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsPreMetric._.antisym
d_antisym_118 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_118 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_118 T_IsPreMetric_104
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))
-- Function.Metric.Structures.IsPreMetric._.cong
d_cong_120 ::
  T_IsPreMetric_104 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_120 :: T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_120 T_IsPreMetric_104
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0))
-- Function.Metric.Structures.IsPreMetric._.isEquivalence
d_isEquivalence_122 ::
  T_IsPreMetric_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_122 :: T_IsPreMetric_104 -> T_IsEquivalence_28
d_isEquivalence_122 T_IsPreMetric_104
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0))))
-- Function.Metric.Structures.IsPreMetric._.isPartialOrder
d_isPartialOrder_124 ::
  T_IsPreMetric_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_124 :: T_IsPreMetric_104 -> T_IsPartialOrder_248
d_isPartialOrder_124 T_IsPreMetric_104
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0))
-- Function.Metric.Structures.IsPreMetric._.isPreorder
d_isPreorder_126 ::
  T_IsPreMetric_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_126 :: T_IsPreMetric_104 -> T_IsPreorder_76
d_isPreorder_126 T_IsPreMetric_104
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))
-- Function.Metric.Structures.IsPreMetric._.nonNegative
d_nonNegative_128 ::
  T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_128 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_128 T_IsPreMetric_104
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0))
-- Function.Metric.Structures.IsPreMetric._.refl
d_refl_130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsPreMetric_104 -> AgdaAny -> AgdaAny
d_refl_130 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
d_refl_130 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_104
v12
  = T_IsPreMetric_104 -> AgdaAny -> AgdaAny
du_refl_130 T_IsPreMetric_104
v12
du_refl_130 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny
du_refl_130 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny
du_refl_130 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Function.Metric.Structures.IsPreMetric._.reflexive
d_reflexive_132 ::
  T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_132 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_132 T_IsPreMetric_104
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0))))
-- Function.Metric.Structures.IsPreMetric._.trans
d_trans_134 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_134 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_134 T_IsPreMetric_104
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0))))
-- Function.Metric.Structures.IsPreMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_136 ::
  T_IsPreMetric_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_136 :: T_IsPreMetric_104 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_136 T_IsPreMetric_104
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0))
-- Function.Metric.Structures.IsPreMetric._.∼-resp-≈
d_'8764''45'resp'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_104 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_138 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> T_Σ_14
d_'8764''45'resp'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_104
v12
  = T_IsPreMetric_104 -> T_Σ_14
du_'8764''45'resp'45''8776'_138 T_IsPreMetric_104
v12
du_'8764''45'resp'45''8776'_138 ::
  T_IsPreMetric_104 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_138 :: T_IsPreMetric_104 -> T_Σ_14
du_'8764''45'resp'45''8776'_138 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Function.Metric.Structures.IsPreMetric._.∼-respʳ-≈
d_'8764''45'resp'691''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_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_140 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''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_104
v12
  = T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_140 T_IsPreMetric_104
v12
du_'8764''45'resp'691''45''8776'_140 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_140 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_140 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Function.Metric.Structures.IsPreMetric._.∼-respˡ-≈
d_'8764''45'resp'737''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_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_142 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''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_104
v12
  = T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_142 T_IsPreMetric_104
v12
du_'8764''45'resp'737''45''8776'_142 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_142 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_142 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Function.Metric.Structures.IsPreMetric._.≲-resp-≈
d_'8818''45'resp'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_104 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_144 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> T_Σ_14
d_'8818''45'resp'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_104
v12
  = T_IsPreMetric_104 -> T_Σ_14
du_'8818''45'resp'45''8776'_144 T_IsPreMetric_104
v12
du_'8818''45'resp'45''8776'_144 ::
  T_IsPreMetric_104 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_144 :: T_IsPreMetric_104 -> T_Σ_14
du_'8818''45'resp'45''8776'_144 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Function.Metric.Structures.IsPreMetric._.≲-respʳ-≈
d_'8818''45'resp'691''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_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_146 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''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_104
v12
  = T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_146 T_IsPreMetric_104
v12
du_'8818''45'resp'691''45''8776'_146 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_146 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_146 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Function.Metric.Structures.IsPreMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_148 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_148 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_104
v12
  = T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_148 T_IsPreMetric_104
v12
du_'8818''45'resp'737''45''8776'_148 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_148 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_148 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Function.Metric.Structures.IsPreMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_152 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_152 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_104
v12
  = T_IsPreMetric_104 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_152 T_IsPreMetric_104
v12
du_isPartialEquivalence_152 ::
  T_IsPreMetric_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_152 :: T_IsPreMetric_104 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_152 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_154 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny
d_refl_154 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny
d_refl_154 T_IsPreMetric_104
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))
-- Function.Metric.Structures.IsPreMetric._.EqC.reflexive
d_reflexive_156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_104 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_156 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_156 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsPreMetric_104
v12
  = T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_156 T_IsPreMetric_104
v12
du_reflexive_156 ::
  T_IsPreMetric_104 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_156 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_156 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_158 ::
  T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_158 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_158 T_IsPreMetric_104
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))
-- Function.Metric.Structures.IsPreMetric._.EqC.trans
d_trans_160 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_160 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_160 T_IsPreMetric_104
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))
-- Function.Metric.Structures.IsPreMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_164 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_164 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsPreMetric_104
v12
  = T_IsPreMetric_104 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_164 T_IsPreMetric_104
v12
du_isPartialEquivalence_164 ::
  T_IsPreMetric_104 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_164 :: T_IsPreMetric_104 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_164 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                  (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.refl
d_refl_166 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny
d_refl_166 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny
d_refl_166 T_IsPreMetric_104
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.reflexive
d_reflexive_168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_104 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_168 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreMetric_104
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_168 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsPreMetric_104
v12
  = T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_168 T_IsPreMetric_104
v12
du_reflexive_168 ::
  T_IsPreMetric_104 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_168 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_168 T_IsPreMetric_104
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                    (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3))
                 AgdaAny
v4)))
-- Function.Metric.Structures.IsPreMetric._.Eq.sym
d_sym_170 ::
  T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_170 :: T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_170 T_IsPreMetric_104
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))))
-- Function.Metric.Structures.IsPreMetric._.Eq.trans
d_trans_172 ::
  T_IsPreMetric_104 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_172 :: T_IsPreMetric_104
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_172 T_IsPreMetric_104
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42 ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric
d_IsQuasiSemiMetric_178 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsQuasiSemiMetric_178 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_178
  = C_constructor_252 T_IsPreMetric_104
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsQuasiSemiMetric.isPreMetric
d_isPreMetric_186 :: T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 :: T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 T_IsQuasiSemiMetric_178
v0
  = case T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0 of
      C_constructor_252 T_IsPreMetric_104
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1
      T_IsQuasiSemiMetric_178
_ -> T_IsPreMetric_104
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsQuasiSemiMetric.0⇒≈
d_0'8658''8776'_188 ::
  T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_188 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_188 T_IsQuasiSemiMetric_178
v0
  = case T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0 of
      C_constructor_252 T_IsPreMetric_104
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_178
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsQuasiSemiMetric._.antisym
d_antisym_192 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_192 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_192 T_IsQuasiSemiMetric_178
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.cong
d_cong_194 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_194 :: T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_194 T_IsQuasiSemiMetric_178
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isEquivalence
d_isEquivalence_196 ::
  T_IsQuasiSemiMetric_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_196 :: T_IsQuasiSemiMetric_178 -> T_IsEquivalence_28
d_isEquivalence_196 T_IsQuasiSemiMetric_178
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isPartialOrder
d_isPartialOrder_198 ::
  T_IsQuasiSemiMetric_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_198 :: T_IsQuasiSemiMetric_178 -> T_IsPartialOrder_248
d_isPartialOrder_198 T_IsQuasiSemiMetric_178
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isPreorder
d_isPreorder_200 ::
  T_IsQuasiSemiMetric_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_200 :: T_IsQuasiSemiMetric_178 -> T_IsPreorder_76
d_isPreorder_200 T_IsQuasiSemiMetric_178
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.isProtoMetric
d_isProtoMetric_202 ::
  T_IsQuasiSemiMetric_178 -> T_IsProtoMetric_30
d_isProtoMetric_202 :: T_IsQuasiSemiMetric_178 -> T_IsProtoMetric_30
d_isProtoMetric_202 T_IsQuasiSemiMetric_178
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))
-- Function.Metric.Structures.IsQuasiSemiMetric._.nonNegative
d_nonNegative_204 ::
  T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_204 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_204 T_IsQuasiSemiMetric_178
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.refl
d_refl_206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_178 -> AgdaAny -> AgdaAny
d_refl_206 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
d_refl_206 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_178
v12
  = T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny
du_refl_206 T_IsQuasiSemiMetric_178
v12
du_refl_206 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny
du_refl_206 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny
du_refl_206 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.reflexive
d_reflexive_208 ::
  T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_208 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_208 T_IsQuasiSemiMetric_178
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.trans
d_trans_210 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_210 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_210 T_IsQuasiSemiMetric_178
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_212 ::
  T_IsQuasiSemiMetric_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_212 :: T_IsQuasiSemiMetric_178 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_212 T_IsQuasiSemiMetric_178
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0)))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≈⇒0
d_'8776''8658'0_214 ::
  T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_214 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_214 T_IsQuasiSemiMetric_178
v0
  = (T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_114 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-resp-≈
d_'8764''45'resp'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_178 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_216 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> T_Σ_14
d_'8764''45'resp'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_178
v12
  = T_IsQuasiSemiMetric_178 -> T_Σ_14
du_'8764''45'resp'45''8776'_216 T_IsQuasiSemiMetric_178
v12
du_'8764''45'resp'45''8776'_216 ::
  T_IsQuasiSemiMetric_178 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_216 :: T_IsQuasiSemiMetric_178 -> T_Σ_14
du_'8764''45'resp'45''8776'_216 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''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_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_218 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''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_178
v12
  = T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_218 T_IsQuasiSemiMetric_178
v12
du_'8764''45'resp'691''45''8776'_218 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_218 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_218 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''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_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_220 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''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_178
v12
  = T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_220 T_IsQuasiSemiMetric_178
v12
du_'8764''45'resp'737''45''8776'_220 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_220 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_220 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≲-resp-≈
d_'8818''45'resp'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_178 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_222 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> T_Σ_14
d_'8818''45'resp'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_178
v12
  = T_IsQuasiSemiMetric_178 -> T_Σ_14
du_'8818''45'resp'45''8776'_222 T_IsQuasiSemiMetric_178
v12
du_'8818''45'resp'45''8776'_222 ::
  T_IsQuasiSemiMetric_178 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_222 :: T_IsQuasiSemiMetric_178 -> T_Σ_14
du_'8818''45'resp'45''8776'_222 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_224 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_224 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsQuasiSemiMetric_178
v12
  = T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_224 T_IsQuasiSemiMetric_178
v12
du_'8818''45'resp'691''45''8776'_224 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_224 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_224 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_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_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_226 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_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_178
v12
  = T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_226 T_IsQuasiSemiMetric_178
v12
du_'8818''45'resp'737''45''8776'_226 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_226 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_226 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_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_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_230 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_178
v12
  = T_IsQuasiSemiMetric_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_IsQuasiSemiMetric_178
v12
du_isPartialEquivalence_230 ::
  T_IsQuasiSemiMetric_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_230 :: T_IsQuasiSemiMetric_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_232 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny
d_refl_232 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny
d_refl_232 T_IsQuasiSemiMetric_178
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.reflexive
d_reflexive_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_178 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_234 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_234 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsQuasiSemiMetric_178
v12
  = T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_234 T_IsQuasiSemiMetric_178
v12
du_reflexive_234 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_234 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_234 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_236 ::
  T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 T_IsQuasiSemiMetric_178
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.EqC.trans
d_trans_238 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 T_IsQuasiSemiMetric_178
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_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_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_242 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_178
v12
  = T_IsQuasiSemiMetric_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_242 T_IsQuasiSemiMetric_178
v12
du_isPartialEquivalence_242 ::
  T_IsQuasiSemiMetric_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_242 :: T_IsQuasiSemiMetric_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_242 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v4
                   = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                       (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                     (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v4))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.refl
d_refl_244 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny
d_refl_244 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny
d_refl_244 T_IsQuasiSemiMetric_178
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.reflexive
d_reflexive_246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsQuasiSemiMetric_178 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_246 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasiSemiMetric_178
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_246 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsQuasiSemiMetric_178
v12
  = T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_246 T_IsQuasiSemiMetric_178
v12
du_reflexive_246 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_246 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_246 T_IsQuasiSemiMetric_178
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v4
                   = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                       (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                       (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v4))
                    AgdaAny
v5))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.sym
d_sym_248 ::
  T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_248 :: T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_248 T_IsQuasiSemiMetric_178
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))))
-- Function.Metric.Structures.IsQuasiSemiMetric._.Eq.trans
d_trans_250 ::
  T_IsQuasiSemiMetric_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_250 :: T_IsQuasiSemiMetric_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_250 T_IsQuasiSemiMetric_178
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v0))))))
-- Function.Metric.Structures.IsSemiMetric
d_IsSemiMetric_256 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsSemiMetric_256 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_256
  = C_constructor_334 T_IsQuasiSemiMetric_178
                      (AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsSemiMetric.isQuasiSemiMetric
d_isQuasiSemiMetric_264 ::
  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 :: T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 T_IsSemiMetric_256
v0
  = case T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0 of
      C_constructor_334 T_IsQuasiSemiMetric_178
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1
      T_IsSemiMetric_256
_ -> T_IsQuasiSemiMetric_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsSemiMetric.sym
d_sym_266 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_266 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_266 T_IsSemiMetric_256
v0
  = case T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0 of
      C_constructor_334 T_IsQuasiSemiMetric_178
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemiMetric_256
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsSemiMetric._.0⇒≈
d_0'8658''8776'_270 ::
  T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_270 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_270 T_IsSemiMetric_256
v0
  = (T_IsQuasiSemiMetric_178
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_188 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))
-- Function.Metric.Structures.IsSemiMetric._.antisym
d_antisym_272 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_272 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_272 T_IsSemiMetric_256
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.cong
d_cong_274 ::
  T_IsSemiMetric_256 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_274 :: T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_274 T_IsSemiMetric_256
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))))
-- Function.Metric.Structures.IsSemiMetric._.isEquivalence
d_isEquivalence_276 ::
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_276 :: T_IsSemiMetric_256 -> T_IsEquivalence_28
d_isEquivalence_276 T_IsSemiMetric_256
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.isPartialOrder
d_isPartialOrder_278 ::
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_278 :: T_IsSemiMetric_256 -> T_IsPartialOrder_248
d_isPartialOrder_278 T_IsSemiMetric_256
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))))
-- Function.Metric.Structures.IsSemiMetric._.isPreMetric
d_isPreMetric_280 :: T_IsSemiMetric_256 -> T_IsPreMetric_104
d_isPreMetric_280 :: T_IsSemiMetric_256 -> T_IsPreMetric_104
d_isPreMetric_280 T_IsSemiMetric_256
v0
  = (T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))
-- Function.Metric.Structures.IsSemiMetric._.isPreorder
d_isPreorder_282 ::
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_282 :: T_IsSemiMetric_256 -> T_IsPreorder_76
d_isPreorder_282 T_IsSemiMetric_256
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.isProtoMetric
d_isProtoMetric_284 :: T_IsSemiMetric_256 -> T_IsProtoMetric_30
d_isProtoMetric_284 :: T_IsSemiMetric_256 -> T_IsProtoMetric_30
d_isProtoMetric_284 T_IsSemiMetric_256
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))
-- Function.Metric.Structures.IsSemiMetric._.nonNegative
d_nonNegative_286 ::
  T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_286 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_286 T_IsSemiMetric_256
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))))
-- Function.Metric.Structures.IsSemiMetric._.refl
d_refl_288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
d_refl_288 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
d_refl_288 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_256
v12
  = T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
du_refl_288 T_IsSemiMetric_256
v12
du_refl_288 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
du_refl_288 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
du_refl_288 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.reflexive
d_reflexive_290 ::
  T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_290 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_290 T_IsSemiMetric_256
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.trans
d_trans_292 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_292 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_292 T_IsSemiMetric_256
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))))))
-- Function.Metric.Structures.IsSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_294 ::
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_294 :: T_IsSemiMetric_256 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_294 T_IsSemiMetric_256
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0))))
-- Function.Metric.Structures.IsSemiMetric._.≈⇒0
d_'8776''8658'0_296 ::
  T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_296 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_296 T_IsSemiMetric_256
v0
  = (T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_114
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))
-- Function.Metric.Structures.IsSemiMetric._.∼-resp-≈
d_'8764''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_256 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_298 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> T_Σ_14
d_'8764''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_256
v12
  = T_IsSemiMetric_256 -> T_Σ_14
du_'8764''45'resp'45''8776'_298 T_IsSemiMetric_256
v12
du_'8764''45'resp'45''8776'_298 ::
  T_IsSemiMetric_256 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_298 :: T_IsSemiMetric_256 -> T_Σ_14
du_'8764''45'resp'45''8776'_298 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.∼-respʳ-≈
d_'8764''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_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_300 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''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_256
v12
  = T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_300 T_IsSemiMetric_256
v12
du_'8764''45'resp'691''45''8776'_300 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_300 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_300 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.∼-respˡ-≈
d_'8764''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_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_302 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''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_256
v12
  = T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_302 T_IsSemiMetric_256
v12
du_'8764''45'resp'737''45''8776'_302 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_302 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_302 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_256 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_304 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> T_Σ_14
d_'8818''45'resp'45''8776'_304 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8
                               ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_256
v12
  = T_IsSemiMetric_256 -> T_Σ_14
du_'8818''45'resp'45''8776'_304 T_IsSemiMetric_256
v12
du_'8818''45'resp'45''8776'_304 ::
  T_IsSemiMetric_256 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_304 :: T_IsSemiMetric_256 -> T_Σ_14
du_'8818''45'resp'45''8776'_304 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_306 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_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_256
v12
  = T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_306 T_IsSemiMetric_256
v12
du_'8818''45'resp'691''45''8776'_306 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_306 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_306 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_308 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_308 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7
                                    ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_256
v12
  = T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_308 T_IsSemiMetric_256
v12
du_'8818''45'resp'737''45''8776'_308 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_308 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_308 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_312 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_312 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_256
v12
  = T_IsSemiMetric_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_312 T_IsSemiMetric_256
v12
du_isPartialEquivalence_312 ::
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_312 :: T_IsSemiMetric_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_312 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_314 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
d_refl_314 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
d_refl_314 T_IsSemiMetric_256
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.reflexive
d_reflexive_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_316 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_316 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsSemiMetric_256
v12
  = T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_316 T_IsSemiMetric_256
v12
du_reflexive_316 ::
  T_IsSemiMetric_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_316 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_316 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_318 ::
  T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_318 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_318 T_IsSemiMetric_256
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.EqC.trans
d_trans_320 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_320 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_320 T_IsSemiMetric_256
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_324 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_324 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9
                           ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 T_IsSemiMetric_256
v12
  = T_IsSemiMetric_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_324 T_IsSemiMetric_256
v12
du_isPartialEquivalence_324 ::
  T_IsSemiMetric_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_324 :: T_IsSemiMetric_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_324 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v5
                      = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                          (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                        (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v5)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.refl
d_refl_326 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
d_refl_326 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny
d_refl_326 T_IsSemiMetric_256
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
                  ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.reflexive
d_reflexive_328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemiMetric_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_328 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiMetric_256
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_328 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11
                T_IsSemiMetric_256
v12
  = T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_328 T_IsSemiMetric_256
v12
du_reflexive_328 ::
  T_IsSemiMetric_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_328 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_328 T_IsSemiMetric_256
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v5
                      = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                          (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                          (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v5))
                       AgdaAny
v6)))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.sym
d_sym_330 ::
  T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_330 :: T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_330 T_IsSemiMetric_256
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
                  ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))))
-- Function.Metric.Structures.IsSemiMetric._.Eq.trans
d_trans_332 ::
  T_IsSemiMetric_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_332 :: T_IsSemiMetric_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_332 T_IsSemiMetric_256
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
                  ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric
d_IsGeneralMetric_340 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsGeneralMetric_340 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_340
  = C_constructor_424 T_IsSemiMetric_256
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Metric.Structures.IsGeneralMetric.isSemiMetric
d_isSemiMetric_350 :: T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 :: T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 T_IsGeneralMetric_340
v0
  = case T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0 of
      C_constructor_424 T_IsSemiMetric_256
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1
      T_IsGeneralMetric_340
_ -> T_IsSemiMetric_256
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsGeneralMetric.triangle
d_triangle_352 ::
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_triangle_352 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_triangle_352 T_IsGeneralMetric_340
v0
  = case T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0 of
      C_constructor_424 T_IsSemiMetric_256
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_340
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Structures.IsGeneralMetric._.0⇒≈
d_0'8658''8776'_356 ::
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_356 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_356 T_IsGeneralMetric_340
v0
  = (T_IsQuasiSemiMetric_178
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_0'8658''8776'_188
      ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))
-- Function.Metric.Structures.IsGeneralMetric._.antisym
d_antisym_358 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_358 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_358 T_IsGeneralMetric_340
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.cong
d_cong_360 ::
  T_IsGeneralMetric_340 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_360 :: T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_cong_360 T_IsGeneralMetric_340
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.isEquivalence
d_isEquivalence_362 ::
  T_IsGeneralMetric_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_362 :: T_IsGeneralMetric_340 -> T_IsEquivalence_28
d_isEquivalence_362 T_IsGeneralMetric_340
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.isPartialOrder
d_isPartialOrder_364 ::
  T_IsGeneralMetric_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_364 :: T_IsGeneralMetric_340 -> T_IsPartialOrder_248
d_isPartialOrder_364 T_IsGeneralMetric_340
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.isPreMetric
d_isPreMetric_366 :: T_IsGeneralMetric_340 -> T_IsPreMetric_104
d_isPreMetric_366 :: T_IsGeneralMetric_340 -> T_IsPreMetric_104
d_isPreMetric_366 T_IsGeneralMetric_340
v0
  = (T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> T_IsPreMetric_104
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
      ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))
-- Function.Metric.Structures.IsGeneralMetric._.isPreorder
d_isPreorder_368 ::
  T_IsGeneralMetric_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_368 :: T_IsGeneralMetric_340 -> T_IsPreorder_76
d_isPreorder_368 T_IsGeneralMetric_340
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.isProtoMetric
d_isProtoMetric_370 :: T_IsGeneralMetric_340 -> T_IsProtoMetric_30
d_isProtoMetric_370 :: T_IsGeneralMetric_340 -> T_IsProtoMetric_30
d_isProtoMetric_370 T_IsGeneralMetric_340
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
         ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))
-- Function.Metric.Structures.IsGeneralMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_372 ::
  T_IsGeneralMetric_340 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_372 :: T_IsGeneralMetric_340 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_372 T_IsGeneralMetric_340
v0
  = (T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))
-- Function.Metric.Structures.IsGeneralMetric._.nonNegative
d_nonNegative_374 ::
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_374 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_nonNegative_374 T_IsGeneralMetric_340
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_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.refl
d_refl_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
d_refl_376 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
d_refl_376 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny -> ()
v8 ~AgdaAny -> AgdaAny -> ()
v9 ~AgdaAny
v10 ~AgdaAny -> AgdaAny -> AgdaAny
v11 ~AgdaAny -> AgdaAny -> AgdaAny
v12
           T_IsGeneralMetric_340
v13
  = T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
du_refl_376 T_IsGeneralMetric_340
v13
du_refl_376 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
du_refl_376 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
du_refl_376 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
                     ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                        (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.reflexive
d_reflexive_378 ::
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_378 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_378 T_IsGeneralMetric_340
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.sym
d_sym_380 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_380 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_380 T_IsGeneralMetric_340
v0 = (T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_266 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))
-- Function.Metric.Structures.IsGeneralMetric._.trans
d_trans_382 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_382 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_382 T_IsGeneralMetric_340
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_384 ::
  T_IsGeneralMetric_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_384 :: T_IsGeneralMetric_340 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_384 T_IsGeneralMetric_340
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0)))))
-- Function.Metric.Structures.IsGeneralMetric._.≈⇒0
d_'8776''8658'0_386 ::
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_386 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_386 T_IsGeneralMetric_340
v0
  = (T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreMetric_104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8776''8658'0_114
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
         ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-resp-≈
d_'8764''45'resp'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_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_388 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> T_Σ_14
d_'8764''45'resp'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_340
v13
  = T_IsGeneralMetric_340 -> T_Σ_14
du_'8764''45'resp'45''8776'_388 T_IsGeneralMetric_340
v13
du_'8764''45'resp'45''8776'_388 ::
  T_IsGeneralMetric_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_388 :: T_IsGeneralMetric_340 -> T_Σ_14
du_'8764''45'resp'45''8776'_388 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
                     ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                        (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-respʳ-≈
d_'8764''45'resp'691''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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_390 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''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_340
v13
  = T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_390 T_IsGeneralMetric_340
v13
du_'8764''45'resp'691''45''8776'_390 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_390 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_390 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
                     ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                        (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_392 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_392 ~()
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_340
v13
  = T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_392 T_IsGeneralMetric_340
v13
du_'8764''45'resp'737''45''8776'_392 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_392 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_392 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
                     ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                        (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_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_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_394 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> T_Σ_14
d_'8818''45'resp'45''8776'_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_340
v13
  = T_IsGeneralMetric_340 -> T_Σ_14
du_'8818''45'resp'45''8776'_394 T_IsGeneralMetric_340
v13
du_'8818''45'resp'45''8776'_394 ::
  T_IsGeneralMetric_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_394 :: T_IsGeneralMetric_340 -> T_Σ_14
du_'8818''45'resp'45''8776'_394 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
                     ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                        (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_396 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_396 ~()
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_340
v13
  = T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_396 T_IsGeneralMetric_340
v13
du_'8818''45'resp'691''45''8776'_396 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_396 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_396 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
                     ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                        (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_398 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_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_340
v13
  = T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_398 T_IsGeneralMetric_340
v13
du_'8818''45'resp'737''45''8776'_398 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_398 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_398 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
                     ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                        (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v5)))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_402 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_402 ~()
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_340
v13
  = T_IsGeneralMetric_340 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_402 T_IsGeneralMetric_340
v13
du_isPartialEquivalence_402 ::
  T_IsGeneralMetric_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_402 :: T_IsGeneralMetric_340 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_402 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_404 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
d_refl_404 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
d_refl_404 T_IsGeneralMetric_340
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.reflexive
d_reflexive_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_340 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_406 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_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_340
v13
  = T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_406 T_IsGeneralMetric_340
v13
du_reflexive_406 ::
  T_IsGeneralMetric_340 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_406 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_406 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30 -> T_IsEquivalence_28
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_408 ::
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_408 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_408 T_IsGeneralMetric_340
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.EqC.trans
d_trans_410 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_410 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_410 T_IsGeneralMetric_340
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_414 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_414 ~()
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_340
v13
  = T_IsGeneralMetric_340 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_414 T_IsGeneralMetric_340
v13
du_isPartialEquivalence_414 ::
  T_IsGeneralMetric_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_414 :: T_IsGeneralMetric_340 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_414 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v6
                         = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                             (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                        ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                           (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v6))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.refl
d_refl_416 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
d_refl_416 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny
d_refl_416 T_IsGeneralMetric_340
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
                  ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
                     ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.reflexive
d_reflexive_418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_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_340 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_418 :: ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGeneralMetric_340
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_418 ~()
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_340
v13
  = T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_418 T_IsGeneralMetric_340
v13
du_reflexive_418 ::
  T_IsGeneralMetric_340 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_418 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_418 T_IsGeneralMetric_340
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2 = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_104
v3 = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186 (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4 = T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112 (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_248
v5 = T_IsProtoMetric_30 -> T_IsPartialOrder_248
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_76
v6
                         = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                             (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                          ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                             (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v6))
                          AgdaAny
v7))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.sym
d_sym_420 ::
  T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 :: T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 T_IsGeneralMetric_340
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
                  ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
                     ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))))
-- Function.Metric.Structures.IsGeneralMetric._.Eq.trans
d_trans_422 ::
  T_IsGeneralMetric_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 :: T_IsGeneralMetric_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 T_IsGeneralMetric_340
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsProtoMetric_30 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsPartialOrder_248
d_isPartialOrder_42
               ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreMetric_104 -> T_IsProtoMetric_30
d_isProtoMetric_112
                  ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
d_isPreMetric_186
                     ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_264 ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340 -> T_IsSemiMetric_256
d_isSemiMetric_350 (T_IsGeneralMetric_340 -> AgdaAny
forall a b. a -> b
coe T_IsGeneralMetric_340
v0))))))))