{-# 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.Nat.Bundles where

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

-- Function.Metric.Nat.Bundles.ProtoMetric
d_ProtoMetric_12 :: p -> p -> ()
d_ProtoMetric_12 p
a0 p
a1 = ()
data T_ProtoMetric_12
  = C_constructor_92 (AgdaAny -> AgdaAny -> Integer)
                     MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
-- Function.Metric.Nat.Bundles.ProtoMetric.Carrier
d_Carrier_26 :: T_ProtoMetric_12 -> ()
d_Carrier_26 :: T_ProtoMetric_12 -> ()
d_Carrier_26 = T_ProtoMetric_12 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._≈_
d__'8776'__28 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> ()
d__'8776'__28 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> ()
d__'8776'__28 = T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric.d
d_d_30 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> Integer
d_d_30 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> Integer
d_d_30 T_ProtoMetric_12
v0
  = case T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0 of
      C_constructor_92 AgdaAny -> AgdaAny -> Integer
v3 T_IsProtoMetric_30
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_ProtoMetric_12
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.ProtoMetric.isProtoMetric
d_isProtoMetric_32 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_32 :: T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 T_ProtoMetric_12
v0
  = case T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0 of
      C_constructor_92 AgdaAny -> AgdaAny -> Integer
v3 T_IsProtoMetric_30
v4 -> T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v4
      T_ProtoMetric_12
_ -> T_IsProtoMetric_30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.ProtoMetric._.antisym
d_antisym_36 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_36 :: T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_36 = T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.cong
d_cong_38 ::
  T_ProtoMetric_12 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_38 :: T_ProtoMetric_12
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_38 = T_ProtoMetric_12
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.isEquivalence
d_isEquivalence_40 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_40 :: T_ProtoMetric_12 -> T_IsEquivalence_28
d_isEquivalence_40 T_ProtoMetric_12
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.isPartialOrder
d_isPartialOrder_42 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_42 :: T_ProtoMetric_12 -> T_IsPartialOrder_248
d_isPartialOrder_42 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))
-- Function.Metric.Nat.Bundles.ProtoMetric._.isPreorder
d_isPreorder_44 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_44 :: T_ProtoMetric_12 -> T_IsPreorder_76
d_isPreorder_44 T_ProtoMetric_12
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0)))
-- Function.Metric.Nat.Bundles.ProtoMetric._.nonNegative
d_nonNegative_46 ::
  T_ProtoMetric_12 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_46 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_46 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))
-- Function.Metric.Nat.Bundles.ProtoMetric._.refl
d_refl_48 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_48 :: () -> () -> T_ProtoMetric_12 -> Integer -> T__'8804'__22
d_refl_48 ~()
v0 ~()
v1 T_ProtoMetric_12
v2 = T_ProtoMetric_12 -> Integer -> T__'8804'__22
du_refl_48 T_ProtoMetric_12
v2
du_refl_48 ::
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_48 :: T_ProtoMetric_12 -> Integer -> T__'8804'__22
du_refl_48 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.reflexive
d_reflexive_50 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_50 :: T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_50 T_ProtoMetric_12
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.trans
d_trans_52 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_52 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_52 T_ProtoMetric_12
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_54 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_54 :: T_ProtoMetric_12 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_54 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
      ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))
-- Function.Metric.Nat.Bundles.ProtoMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_56 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_56 :: () -> () -> T_ProtoMetric_12 -> T_Σ_14
d_'8764''45'resp'45''8776'_56 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_Σ_14
du_'8764''45'resp'45''8776'_56 T_ProtoMetric_12
v2
du_'8764''45'resp'45''8776'_56 ::
  T_ProtoMetric_12 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_56 :: T_ProtoMetric_12 -> T_Σ_14
du_'8764''45'resp'45''8776'_56 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_58 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_58 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_58 T_ProtoMetric_12
v2
du_'8764''45'resp'691''45''8776'_58 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_58 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_58 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_60 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_60 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_60 T_ProtoMetric_12
v2
du_'8764''45'resp'737''45''8776'_60 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_60 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_60 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_62 :: () -> () -> T_ProtoMetric_12 -> T_Σ_14
d_'8818''45'resp'45''8776'_62 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_Σ_14
du_'8818''45'resp'45''8776'_62 T_ProtoMetric_12
v2
du_'8818''45'resp'45''8776'_62 ::
  T_ProtoMetric_12 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_62 :: T_ProtoMetric_12 -> T_Σ_14
du_'8818''45'resp'45''8776'_62 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_64 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_64 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_64 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_64 T_ProtoMetric_12
v2
du_'8818''45'resp'691''45''8776'_64 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_64 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_64 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_66 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_66 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_66 T_ProtoMetric_12
v2
du_'8818''45'resp'737''45''8776'_66 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_66 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_66 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_70 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_70 :: () -> () -> T_ProtoMetric_12 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_70 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_70 T_ProtoMetric_12
v2
du_isPartialEquivalence_70 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_70 :: T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_70 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
            (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v1)))
-- Function.Metric.Nat.Bundles.ProtoMetric._.EqC.refl
d_refl_72 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny
d_refl_72 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny
d_refl_72 T_ProtoMetric_12
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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0)))
-- Function.Metric.Nat.Bundles.ProtoMetric._.EqC.reflexive
d_reflexive_74 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_74 :: ()
-> ()
-> T_ProtoMetric_12
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_74 ~()
v0 ~()
v1 T_ProtoMetric_12
v2 = T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_74 T_ProtoMetric_12
v2
du_reflexive_74 ::
  T_ProtoMetric_12 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_74 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_74 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
              (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v1))
           AgdaAny
v2)
-- Function.Metric.Nat.Bundles.ProtoMetric._.EqC.sym
d_sym_76 ::
  T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_76 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_76 T_ProtoMetric_12
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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0)))
-- Function.Metric.Nat.Bundles.ProtoMetric._.EqC.trans
d_trans_78 ::
  T_ProtoMetric_12 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_78 :: T_ProtoMetric_12
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_78 T_ProtoMetric_12
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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0)))
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_82 :: () -> () -> T_ProtoMetric_12 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_82 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_82 T_ProtoMetric_12
v2
du_isPartialEquivalence_82 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_82 :: T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_82 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.ProtoMetric._.Eq.refl
d_refl_84 ::
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_84 :: T_ProtoMetric_12 -> Integer -> T__'8801'__12
d_refl_84 = T_ProtoMetric_12 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.reflexive
d_reflexive_86 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_86 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_86 = ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.sym
d_sym_88 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_88 :: T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_88 = T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.trans
d_trans_90 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_90 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_90 = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric
d_PreMetric_98 :: p -> p -> ()
d_PreMetric_98 p
a0 p
a1 = ()
data T_PreMetric_98
  = C_constructor_184 (AgdaAny -> AgdaAny -> Integer)
                      MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_104
-- Function.Metric.Nat.Bundles.PreMetric.Carrier
d_Carrier_112 :: T_PreMetric_98 -> ()
d_Carrier_112 :: T_PreMetric_98 -> ()
d_Carrier_112 = T_PreMetric_98 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._≈_
d__'8776'__114 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> ()
d__'8776'__114 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> ()
d__'8776'__114 = T_PreMetric_98 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric.d
d_d_116 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> Integer
d_d_116 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> Integer
d_d_116 T_PreMetric_98
v0
  = case T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0 of
      C_constructor_184 AgdaAny -> AgdaAny -> Integer
v3 T_IsPreMetric_104
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_PreMetric_98
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.PreMetric.isPreMetric
d_isPreMetric_118 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_104
d_isPreMetric_118 :: T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 T_PreMetric_98
v0
  = case T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0 of
      C_constructor_184 AgdaAny -> AgdaAny -> Integer
v3 T_IsPreMetric_104
v4 -> T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4
      T_PreMetric_98
_ -> T_IsPreMetric_104
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.PreMetric._.antisym
d_antisym_122 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_122 :: T_PreMetric_98
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_122 = T_PreMetric_98
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.cong
d_cong_124 ::
  T_PreMetric_98 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_124 :: T_PreMetric_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_124 = T_PreMetric_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.isEquivalence
d_isEquivalence_126 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_126 :: T_PreMetric_98 -> T_IsEquivalence_28
d_isEquivalence_126 T_PreMetric_98
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.isPartialOrder
d_isPartialOrder_128 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_128 :: T_PreMetric_98 -> T_IsPartialOrder_248
d_isPartialOrder_128 T_PreMetric_98
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.isPreorder
d_isPreorder_130 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_130 :: T_PreMetric_98 -> T_IsPreorder_76
d_isPreorder_130 T_PreMetric_98
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.isProtoMetric
d_isProtoMetric_132 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_132 :: T_PreMetric_98 -> T_IsProtoMetric_30
d_isProtoMetric_132 T_PreMetric_98
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
      ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0))
-- Function.Metric.Nat.Bundles.PreMetric._.nonNegative
d_nonNegative_134 ::
  T_PreMetric_98 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_134 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_134 T_PreMetric_98
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.refl
d_refl_136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_136 :: () -> () -> T_PreMetric_98 -> Integer -> T__'8804'__22
d_refl_136 ~()
v0 ~()
v1 T_PreMetric_98
v2 = T_PreMetric_98 -> Integer -> T__'8804'__22
du_refl_136 T_PreMetric_98
v2
du_refl_136 ::
  T_PreMetric_98 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_136 :: T_PreMetric_98 -> Integer -> T__'8804'__22
du_refl_136 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.reflexive
d_reflexive_138 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_138 :: T_PreMetric_98
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_138 T_PreMetric_98
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.trans
d_trans_140 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_140 :: T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_140 T_PreMetric_98
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_142 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_142 :: T_PreMetric_98 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_142 T_PreMetric_98
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.≈⇒0
d_'8776''8658'0_144 ::
  T_PreMetric_98 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_144 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_144 = T_PreMetric_98 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_146 :: () -> () -> T_PreMetric_98 -> T_Σ_14
d_'8764''45'resp'45''8776'_146 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98 -> T_Σ_14
du_'8764''45'resp'45''8776'_146 T_PreMetric_98
v2
du_'8764''45'resp'45''8776'_146 ::
  T_PreMetric_98 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_146 :: T_PreMetric_98 -> T_Σ_14
du_'8764''45'resp'45''8776'_146 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_148 :: ()
-> ()
-> T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_148 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_148 T_PreMetric_98
v2
du_'8764''45'resp'691''45''8776'_148 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_148 :: T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_148 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_150 :: ()
-> ()
-> T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_150 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_150 T_PreMetric_98
v2
du_'8764''45'resp'737''45''8776'_150 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_150 :: T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_150 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_152 :: () -> () -> T_PreMetric_98 -> T_Σ_14
d_'8818''45'resp'45''8776'_152 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98 -> T_Σ_14
du_'8818''45'resp'45''8776'_152 T_PreMetric_98
v2
du_'8818''45'resp'45''8776'_152 ::
  T_PreMetric_98 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_152 :: T_PreMetric_98 -> T_Σ_14
du_'8818''45'resp'45''8776'_152 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_154 :: ()
-> ()
-> T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_154 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_154 T_PreMetric_98
v2
du_'8818''45'resp'691''45''8776'_154 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_154 :: T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_154 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_156 :: ()
-> ()
-> T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_156 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_156 T_PreMetric_98
v2
du_'8818''45'resp'737''45''8776'_156 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_156 :: T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_156 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_160 :: () -> () -> T_PreMetric_98 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_160 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_160 T_PreMetric_98
v2
du_isPartialEquivalence_160 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_160 :: T_PreMetric_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_160 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
               (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v2))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.refl
d_refl_162 :: T_PreMetric_98 -> AgdaAny -> AgdaAny
d_refl_162 :: T_PreMetric_98 -> AgdaAny -> AgdaAny
d_refl_162 T_PreMetric_98
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.reflexive
d_reflexive_164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_164 :: ()
-> ()
-> T_PreMetric_98
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_164 ~()
v0 ~()
v1 T_PreMetric_98
v2 = T_PreMetric_98 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_164 T_PreMetric_98
v2
du_reflexive_164 ::
  T_PreMetric_98 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_164 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_164 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                 (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v2))
              AgdaAny
v3))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.sym
d_sym_166 ::
  T_PreMetric_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_166 :: T_PreMetric_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_166 T_PreMetric_98
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.trans
d_trans_168 ::
  T_PreMetric_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_168 :: T_PreMetric_98
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_168 T_PreMetric_98
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_PreMetric_98 -> T_IsPreMetric_104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_172 :: () -> () -> T_PreMetric_98 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_172 ~()
v0 ~()
v1 T_PreMetric_98
v2
  = T_PreMetric_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_172 T_PreMetric_98
v2
du_isPartialEquivalence_172 ::
  T_PreMetric_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_172 :: T_PreMetric_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_172 T_PreMetric_98
v0
  = let v1 :: T_IsPreMetric_104
v1 = T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.PreMetric._.Eq.refl
d_refl_174 ::
  T_PreMetric_98 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_174 :: T_PreMetric_98 -> Integer -> T__'8801'__12
d_refl_174 = T_PreMetric_98 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.reflexive
d_reflexive_176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_176 :: ()
-> ()
-> T_PreMetric_98
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_176 = ()
-> ()
-> T_PreMetric_98
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.sym
d_sym_178 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_178 :: T_PreMetric_98
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_178 = T_PreMetric_98
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.trans
d_trans_180 ::
  T_PreMetric_98 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_180 :: T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_180 = T_PreMetric_98
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric.protoMetric
d_protoMetric_182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_98 -> T_ProtoMetric_12
d_protoMetric_182 :: () -> () -> T_PreMetric_98 -> T_ProtoMetric_12
d_protoMetric_182 ~()
v0 ~()
v1 T_PreMetric_98
v2 = T_PreMetric_98 -> T_ProtoMetric_12
du_protoMetric_182 T_PreMetric_98
v2
du_protoMetric_182 :: T_PreMetric_98 -> T_ProtoMetric_12
du_protoMetric_182 :: T_PreMetric_98 -> T_ProtoMetric_12
du_protoMetric_182 T_PreMetric_98
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsProtoMetric_30 -> T_ProtoMetric_12)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsProtoMetric_30
-> T_ProtoMetric_12
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsProtoMetric_30 -> T_ProtoMetric_12
C_constructor_92 (T_PreMetric_98 -> AgdaAny -> AgdaAny -> Integer
d_d_116 (T_PreMetric_98 -> T_PreMetric_98
forall a b. a -> b
coe T_PreMetric_98
v0))
      (T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_PreMetric_98 -> T_IsPreMetric_104)
-> AgdaAny -> T_IsPreMetric_104
forall a b. a -> b
coe T_PreMetric_98 -> T_IsPreMetric_104
d_isPreMetric_118 (T_PreMetric_98 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric
d_QuasiSemiMetric_190 :: p -> p -> ()
d_QuasiSemiMetric_190 p
a0 p
a1 = ()
data T_QuasiSemiMetric_190
  = C_constructor_284 (AgdaAny -> AgdaAny -> Integer)
                      MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_178
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.Carrier
d_Carrier_204 :: T_QuasiSemiMetric_190 -> ()
d_Carrier_204 :: T_QuasiSemiMetric_190 -> ()
d_Carrier_204 = T_QuasiSemiMetric_190 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._≈_
d__'8776'__206 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> ()
d__'8776'__206 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> ()
d__'8776'__206 = T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.d
d_d_208 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> Integer
d_d_208 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> Integer
d_d_208 T_QuasiSemiMetric_190
v0
  = case T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0 of
      C_constructor_284 AgdaAny -> AgdaAny -> Integer
v3 T_IsQuasiSemiMetric_178
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_QuasiSemiMetric_190
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.isQuasiSemiMetric
d_isQuasiSemiMetric_210 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 :: T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 T_QuasiSemiMetric_190
v0
  = case T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0 of
      C_constructor_284 AgdaAny -> AgdaAny -> Integer
v3 T_IsQuasiSemiMetric_178
v4 -> T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v4
      T_QuasiSemiMetric_190
_ -> T_IsQuasiSemiMetric_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.0⇒≈
d_0'8658''8776'_214 ::
  T_QuasiSemiMetric_190 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_214 :: T_QuasiSemiMetric_190
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_214 T_QuasiSemiMetric_190
v0
  = (T_IsQuasiSemiMetric_178
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_188
      ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.antisym
d_antisym_216 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_216 :: T_QuasiSemiMetric_190
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_216 = T_QuasiSemiMetric_190
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.cong
d_cong_218 ::
  T_QuasiSemiMetric_190 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_218 :: T_QuasiSemiMetric_190
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_218 = T_QuasiSemiMetric_190
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isEquivalence
d_isEquivalence_220 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_220 :: T_QuasiSemiMetric_190 -> T_IsEquivalence_28
d_isEquivalence_220 T_QuasiSemiMetric_190
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPartialOrder
d_isPartialOrder_222 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_222 :: T_QuasiSemiMetric_190 -> T_IsPartialOrder_248
d_isPartialOrder_222 T_QuasiSemiMetric_190
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPreMetric
d_isPreMetric_224 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_104
d_isPreMetric_224 :: T_QuasiSemiMetric_190 -> T_IsPreMetric_104
d_isPreMetric_224 T_QuasiSemiMetric_190
v0
  = (T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> T_IsPreMetric_104
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
      ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPreorder
d_isPreorder_226 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_226 :: T_QuasiSemiMetric_190 -> T_IsPreorder_76
d_isPreorder_226 T_QuasiSemiMetric_190
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isProtoMetric
d_isProtoMetric_228 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_228 :: T_QuasiSemiMetric_190 -> T_IsProtoMetric_30
d_isProtoMetric_228 T_QuasiSemiMetric_190
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
         ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.nonNegative
d_nonNegative_230 ::
  T_QuasiSemiMetric_190 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_230 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_230 T_QuasiSemiMetric_190
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.refl
d_refl_232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_232 :: () -> () -> T_QuasiSemiMetric_190 -> Integer -> T__'8804'__22
d_refl_232 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2 = T_QuasiSemiMetric_190 -> Integer -> T__'8804'__22
du_refl_232 T_QuasiSemiMetric_190
v2
du_refl_232 ::
  T_QuasiSemiMetric_190 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_232 :: T_QuasiSemiMetric_190 -> Integer -> T__'8804'__22
du_refl_232 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.reflexive
d_reflexive_234 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_234 :: T_QuasiSemiMetric_190
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_234 T_QuasiSemiMetric_190
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.trans
d_trans_236 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_236 :: T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_236 T_QuasiSemiMetric_190
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_238 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_238 :: T_QuasiSemiMetric_190 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_238 T_QuasiSemiMetric_190
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≈⇒0
d_'8776''8658'0_240 ::
  T_QuasiSemiMetric_190 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_240 :: T_QuasiSemiMetric_190
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_240 = T_QuasiSemiMetric_190
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_242 :: () -> () -> T_QuasiSemiMetric_190 -> T_Σ_14
d_'8764''45'resp'45''8776'_242 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190 -> T_Σ_14
du_'8764''45'resp'45''8776'_242 T_QuasiSemiMetric_190
v2
du_'8764''45'resp'45''8776'_242 ::
  T_QuasiSemiMetric_190 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_242 :: T_QuasiSemiMetric_190 -> T_Σ_14
du_'8764''45'resp'45''8776'_242 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_244 :: ()
-> ()
-> T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_244 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_244 T_QuasiSemiMetric_190
v2
du_'8764''45'resp'691''45''8776'_244 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_244 :: T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_244 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_246 :: ()
-> ()
-> T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_246 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_246 T_QuasiSemiMetric_190
v2
du_'8764''45'resp'737''45''8776'_246 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_246 :: T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_246 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_248 :: () -> () -> T_QuasiSemiMetric_190 -> T_Σ_14
d_'8818''45'resp'45''8776'_248 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190 -> T_Σ_14
du_'8818''45'resp'45''8776'_248 T_QuasiSemiMetric_190
v2
du_'8818''45'resp'45''8776'_248 ::
  T_QuasiSemiMetric_190 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_248 :: T_QuasiSemiMetric_190 -> T_Σ_14
du_'8818''45'resp'45''8776'_248 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_250 :: ()
-> ()
-> T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_250 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_250 T_QuasiSemiMetric_190
v2
du_'8818''45'resp'691''45''8776'_250 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_250 :: T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_250 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_252 :: ()
-> ()
-> T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_252 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_252 T_QuasiSemiMetric_190
v2
du_'8818''45'resp'737''45''8776'_252 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_252 :: T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_252 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_256 :: () -> () -> T_QuasiSemiMetric_190 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_256 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_256 T_QuasiSemiMetric_190
v2
du_isPartialEquivalence_256 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_256 :: T_QuasiSemiMetric_190 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_256 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                  (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v3)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.refl
d_refl_258 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny
d_refl_258 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny
d_refl_258 T_QuasiSemiMetric_190
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.reflexive
d_reflexive_260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_260 :: ()
-> ()
-> T_QuasiSemiMetric_190
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_260 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2 = T_QuasiSemiMetric_190
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_260 T_QuasiSemiMetric_190
v2
du_reflexive_260 ::
  T_QuasiSemiMetric_190 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_260 :: T_QuasiSemiMetric_190
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_260 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                    (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v3))
                 AgdaAny
v4)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.sym
d_sym_262 ::
  T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_262 :: T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_262 T_QuasiSemiMetric_190
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.trans
d_trans_264 ::
  T_QuasiSemiMetric_190 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_264 :: T_QuasiSemiMetric_190
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_264 T_QuasiSemiMetric_190
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_268 :: () -> () -> T_QuasiSemiMetric_190 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_268 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2
  = T_QuasiSemiMetric_190 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_268 T_QuasiSemiMetric_190
v2
du_isPartialEquivalence_268 ::
  T_QuasiSemiMetric_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_268 :: T_QuasiSemiMetric_190 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_268 T_QuasiSemiMetric_190
v0
  = let v1 :: T_IsQuasiSemiMetric_178
v1 = T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_104
v2
             = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.QuasiSemiMetric._.Eq.refl
d_refl_270 ::
  T_QuasiSemiMetric_190 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_270 :: T_QuasiSemiMetric_190 -> Integer -> T__'8801'__12
d_refl_270 = T_QuasiSemiMetric_190 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.reflexive
d_reflexive_272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_272 :: ()
-> ()
-> T_QuasiSemiMetric_190
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_272 = ()
-> ()
-> T_QuasiSemiMetric_190
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.sym
d_sym_274 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_274 :: T_QuasiSemiMetric_190
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_274 = T_QuasiSemiMetric_190
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.trans
d_trans_276 ::
  T_QuasiSemiMetric_190 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_276 :: T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_276 = T_QuasiSemiMetric_190
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.preMetric
d_preMetric_278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 -> T_PreMetric_98
d_preMetric_278 :: () -> () -> T_QuasiSemiMetric_190 -> T_PreMetric_98
d_preMetric_278 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2 = T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 T_QuasiSemiMetric_190
v2
du_preMetric_278 :: T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 :: T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 T_QuasiSemiMetric_190
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsPreMetric_104 -> T_PreMetric_98)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsPreMetric_104
-> T_PreMetric_98
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsPreMetric_104 -> T_PreMetric_98
C_constructor_184 (T_QuasiSemiMetric_190 -> AgdaAny -> AgdaAny -> Integer
d_d_208 (T_QuasiSemiMetric_190 -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))
      (T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
         ((T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_210 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.protoMetric
d_protoMetric_282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_190 -> T_ProtoMetric_12
d_protoMetric_282 :: () -> () -> T_QuasiSemiMetric_190 -> T_ProtoMetric_12
d_protoMetric_282 ~()
v0 ~()
v1 T_QuasiSemiMetric_190
v2 = T_QuasiSemiMetric_190 -> T_ProtoMetric_12
du_protoMetric_282 T_QuasiSemiMetric_190
v2
du_protoMetric_282 :: T_QuasiSemiMetric_190 -> T_ProtoMetric_12
du_protoMetric_282 :: T_QuasiSemiMetric_190 -> T_ProtoMetric_12
du_protoMetric_282 T_QuasiSemiMetric_190
v0
  = (T_PreMetric_98 -> T_ProtoMetric_12) -> AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe T_PreMetric_98 -> T_ProtoMetric_12
du_protoMetric_182 ((T_QuasiSemiMetric_190 -> T_PreMetric_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 (T_QuasiSemiMetric_190 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190
v0))
-- Function.Metric.Nat.Bundles.SemiMetric
d_SemiMetric_290 :: p -> p -> ()
d_SemiMetric_290 p
a0 p
a1 = ()
data T_SemiMetric_290
  = C_constructor_390 (AgdaAny -> AgdaAny -> Integer)
                      MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_256
-- Function.Metric.Nat.Bundles.SemiMetric.Carrier
d_Carrier_304 :: T_SemiMetric_290 -> ()
d_Carrier_304 :: T_SemiMetric_290 -> ()
d_Carrier_304 = T_SemiMetric_290 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._≈_
d__'8776'__306 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> ()
d__'8776'__306 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> ()
d__'8776'__306 = T_SemiMetric_290 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric.d
d_d_308 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> Integer
d_d_308 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> Integer
d_d_308 T_SemiMetric_290
v0
  = case T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0 of
      C_constructor_390 AgdaAny -> AgdaAny -> Integer
v3 T_IsSemiMetric_256
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_SemiMetric_290
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.SemiMetric.isSemiMetric
d_isSemiMetric_310 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_256
d_isSemiMetric_310 :: T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 T_SemiMetric_290
v0
  = case T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0 of
      C_constructor_390 AgdaAny -> AgdaAny -> Integer
v3 T_IsSemiMetric_256
v4 -> T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v4
      T_SemiMetric_290
_ -> T_IsSemiMetric_256
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.SemiMetric._.0⇒≈
d_0'8658''8776'_314 ::
  T_SemiMetric_290 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_314 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_314 T_SemiMetric_290
v0
  = (T_IsQuasiSemiMetric_178
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
         ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.antisym
d_antisym_316 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_316 :: T_SemiMetric_290
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_316 = T_SemiMetric_290
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.cong
d_cong_318 ::
  T_SemiMetric_290 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_318 :: T_SemiMetric_290
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_318 = T_SemiMetric_290
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.isEquivalence
d_isEquivalence_320 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_320 :: T_SemiMetric_290 -> T_IsEquivalence_28
d_isEquivalence_320 T_SemiMetric_290
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPartialOrder
d_isPartialOrder_322 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_322 :: T_SemiMetric_290 -> T_IsPartialOrder_248
d_isPartialOrder_322 T_SemiMetric_290
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPreMetric
d_isPreMetric_324 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_104
d_isPreMetric_324 :: T_SemiMetric_290 -> T_IsPreMetric_104
d_isPreMetric_324 T_SemiMetric_290
v0
  = (T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> T_IsPreMetric_104
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
      ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
         ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPreorder
d_isPreorder_326 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_326 :: T_SemiMetric_290 -> T_IsPreorder_76
d_isPreorder_326 T_SemiMetric_290
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isProtoMetric
d_isProtoMetric_328 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_328 :: T_SemiMetric_290 -> T_IsProtoMetric_30
d_isProtoMetric_328 T_SemiMetric_290
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
         ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
            ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_330 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_330 :: T_SemiMetric_290 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_330 T_SemiMetric_290
v0
  = (T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe
      T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
      ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0))
-- Function.Metric.Nat.Bundles.SemiMetric._.nonNegative
d_nonNegative_332 ::
  T_SemiMetric_290 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_332 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_332 T_SemiMetric_290
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.refl
d_refl_334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_334 :: () -> () -> T_SemiMetric_290 -> Integer -> T__'8804'__22
d_refl_334 ~()
v0 ~()
v1 T_SemiMetric_290
v2 = T_SemiMetric_290 -> Integer -> T__'8804'__22
du_refl_334 T_SemiMetric_290
v2
du_refl_334 ::
  T_SemiMetric_290 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_334 :: T_SemiMetric_290 -> Integer -> T__'8804'__22
du_refl_334 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.reflexive
d_reflexive_336 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_336 :: T_SemiMetric_290
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_336 T_SemiMetric_290
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.sym
d_sym_338 ::
  T_SemiMetric_290 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_338 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_338 = T_SemiMetric_290 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.trans
d_trans_340 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_340 :: T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_340 T_SemiMetric_290
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_342 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_342 :: T_SemiMetric_290 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_342 T_SemiMetric_290
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≈⇒0
d_'8776''8658'0_344 ::
  T_SemiMetric_290 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_344 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_344 = T_SemiMetric_290 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_346 :: () -> () -> T_SemiMetric_290 -> T_Σ_14
d_'8764''45'resp'45''8776'_346 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290 -> T_Σ_14
du_'8764''45'resp'45''8776'_346 T_SemiMetric_290
v2
du_'8764''45'resp'45''8776'_346 ::
  T_SemiMetric_290 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_346 :: T_SemiMetric_290 -> T_Σ_14
du_'8764''45'resp'45''8776'_346 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_348 :: ()
-> ()
-> T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_348 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_348 T_SemiMetric_290
v2
du_'8764''45'resp'691''45''8776'_348 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_348 :: T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_348 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_350 :: ()
-> ()
-> T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_350 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_350 T_SemiMetric_290
v2
du_'8764''45'resp'737''45''8776'_350 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_350 :: T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_350 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_352 :: () -> () -> T_SemiMetric_290 -> T_Σ_14
d_'8818''45'resp'45''8776'_352 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290 -> T_Σ_14
du_'8818''45'resp'45''8776'_352 T_SemiMetric_290
v2
du_'8818''45'resp'45''8776'_352 ::
  T_SemiMetric_290 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_352 :: T_SemiMetric_290 -> T_Σ_14
du_'8818''45'resp'45''8776'_352 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_354 :: ()
-> ()
-> T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_354 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_354 T_SemiMetric_290
v2
du_'8818''45'resp'691''45''8776'_354 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_354 :: T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_354 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_356 :: ()
-> ()
-> T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_356 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_356 T_SemiMetric_290
v2
du_'8818''45'resp'737''45''8776'_356 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_356 :: T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_356 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_360 :: () -> () -> T_SemiMetric_290 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_360 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_360 T_SemiMetric_290
v2
du_isPartialEquivalence_360 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_360 :: T_SemiMetric_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_360 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                     (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v4))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.refl
d_refl_362 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny
d_refl_362 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny
d_refl_362 T_SemiMetric_290
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.reflexive
d_reflexive_364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_364 :: ()
-> ()
-> T_SemiMetric_290
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_364 ~()
v0 ~()
v1 T_SemiMetric_290
v2 = T_SemiMetric_290 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_364 T_SemiMetric_290
v2
du_reflexive_364 ::
  T_SemiMetric_290 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_364 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_364 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                       (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v4))
                    AgdaAny
v5))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.sym
d_sym_366 ::
  T_SemiMetric_290 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_366 :: T_SemiMetric_290 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_366 T_SemiMetric_290
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.trans
d_trans_368 ::
  T_SemiMetric_290 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_368 :: T_SemiMetric_290
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_368 T_SemiMetric_290
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_SemiMetric_290 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_372 :: () -> () -> T_SemiMetric_290 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_372 ~()
v0 ~()
v1 T_SemiMetric_290
v2
  = T_SemiMetric_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_372 T_SemiMetric_290
v2
du_isPartialEquivalence_372 ::
  T_SemiMetric_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_372 :: T_SemiMetric_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_372 T_SemiMetric_290
v0
  = let v1 :: T_IsSemiMetric_256
v1 = T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_178
v2
             = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.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.Nat.Bundles.SemiMetric._.Eq.refl
d_refl_374 ::
  T_SemiMetric_290 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_374 :: T_SemiMetric_290 -> Integer -> T__'8801'__12
d_refl_374 = T_SemiMetric_290 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.reflexive
d_reflexive_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_376 :: ()
-> ()
-> T_SemiMetric_290
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_376 = ()
-> ()
-> T_SemiMetric_290
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.sym
d_sym_378 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_378 :: T_SemiMetric_290
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_378 = T_SemiMetric_290
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.trans
d_trans_380 ::
  T_SemiMetric_290 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_380 :: T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_380 = T_SemiMetric_290
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric.quasiSemiMetric
d_quasiSemiMetric_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 -> T_QuasiSemiMetric_190
d_quasiSemiMetric_382 :: () -> () -> T_SemiMetric_290 -> T_QuasiSemiMetric_190
d_quasiSemiMetric_382 ~()
v0 ~()
v1 T_SemiMetric_290
v2 = T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 T_SemiMetric_290
v2
du_quasiSemiMetric_382 :: T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 :: T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 T_SemiMetric_290
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsQuasiSemiMetric_178 -> T_QuasiSemiMetric_190)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsQuasiSemiMetric_178
-> T_QuasiSemiMetric_190
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsQuasiSemiMetric_178 -> T_QuasiSemiMetric_190
C_constructor_284 (T_SemiMetric_290 -> AgdaAny -> AgdaAny -> Integer
d_d_308 (T_SemiMetric_290 -> T_SemiMetric_290
forall a b. a -> b
coe T_SemiMetric_290
v0))
      (T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
         ((T_SemiMetric_290 -> T_IsSemiMetric_256)
-> AgdaAny -> T_IsSemiMetric_256
forall a b. a -> b
coe T_SemiMetric_290 -> T_IsSemiMetric_256
d_isSemiMetric_310 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.preMetric
d_preMetric_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 -> T_PreMetric_98
d_preMetric_386 :: () -> () -> T_SemiMetric_290 -> T_PreMetric_98
d_preMetric_386 ~()
v0 ~()
v1 T_SemiMetric_290
v2 = T_SemiMetric_290 -> T_PreMetric_98
du_preMetric_386 T_SemiMetric_290
v2
du_preMetric_386 :: T_SemiMetric_290 -> T_PreMetric_98
du_preMetric_386 :: T_SemiMetric_290 -> T_PreMetric_98
du_preMetric_386 T_SemiMetric_290
v0
  = (T_QuasiSemiMetric_190 -> T_PreMetric_98)
-> AgdaAny -> T_PreMetric_98
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 ((T_SemiMetric_290 -> T_QuasiSemiMetric_190) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0))
-- Function.Metric.Nat.Bundles.SemiMetric._.protoMetric
d_protoMetric_388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_290 -> T_ProtoMetric_12
d_protoMetric_388 :: () -> () -> T_SemiMetric_290 -> T_ProtoMetric_12
d_protoMetric_388 ~()
v0 ~()
v1 T_SemiMetric_290
v2 = T_SemiMetric_290 -> T_ProtoMetric_12
du_protoMetric_388 T_SemiMetric_290
v2
du_protoMetric_388 :: T_SemiMetric_290 -> T_ProtoMetric_12
du_protoMetric_388 :: T_SemiMetric_290 -> T_ProtoMetric_12
du_protoMetric_388 T_SemiMetric_290
v0
  = let v1 :: AgdaAny
v1 = (T_SemiMetric_290 -> T_QuasiSemiMetric_190) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 (T_SemiMetric_290 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe ((T_PreMetric_98 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_ProtoMetric_12
du_protoMetric_182 ((T_QuasiSemiMetric_190 -> T_PreMetric_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Metric.Nat.Bundles.Metric
d_Metric_396 :: p -> p -> ()
d_Metric_396 p
a0 p
a1 = ()
data T_Metric_396
  = C_constructor_502 (AgdaAny -> AgdaAny -> Integer)
                      MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_340
-- Function.Metric.Nat.Bundles.Metric.Carrier
d_Carrier_410 :: T_Metric_396 -> ()
d_Carrier_410 :: T_Metric_396 -> ()
d_Carrier_410 = T_Metric_396 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._≈_
d__'8776'__412 :: T_Metric_396 -> AgdaAny -> AgdaAny -> ()
d__'8776'__412 :: T_Metric_396 -> AgdaAny -> AgdaAny -> ()
d__'8776'__412 = T_Metric_396 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric.d
d_d_414 :: T_Metric_396 -> AgdaAny -> AgdaAny -> Integer
d_d_414 :: T_Metric_396 -> AgdaAny -> AgdaAny -> Integer
d_d_414 T_Metric_396
v0
  = case T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0 of
      C_constructor_502 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_340
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_Metric_396
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.Metric.isMetric
d_isMetric_416 ::
  T_Metric_396 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_340
d_isMetric_416 :: T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 T_Metric_396
v0
  = case T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0 of
      C_constructor_502 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_340
v4 -> T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v4
      T_Metric_396
_ -> T_IsGeneralMetric_340
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.Metric._.0⇒≈
d_0'8658''8776'_420 ::
  T_Metric_396 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_420 :: T_Metric_396 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_420 T_Metric_396
v0
  = (T_IsQuasiSemiMetric_178
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
         ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
            ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))
-- Function.Metric.Nat.Bundles.Metric._.antisym
d_antisym_422 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_422 :: T_Metric_396
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_422 = T_Metric_396
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.cong
d_cong_424 ::
  T_Metric_396 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_424 :: T_Metric_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_424 = T_Metric_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.isEquivalence
d_isEquivalence_426 ::
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_426 :: T_Metric_396 -> T_IsEquivalence_28
d_isEquivalence_426 T_Metric_396
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                        ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.isPartialOrder
d_isPartialOrder_428 ::
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_428 :: T_Metric_396 -> T_IsPartialOrder_248
d_isPartialOrder_428 T_Metric_396
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                  ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.isPreMetric
d_isPreMetric_430 ::
  T_Metric_396 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_104
d_isPreMetric_430 :: T_Metric_396 -> T_IsPreMetric_104
d_isPreMetric_430 T_Metric_396
v0
  = (T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> T_IsPreMetric_104
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
      ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
         ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
            ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))
-- Function.Metric.Nat.Bundles.Metric._.isPreorder
d_isPreorder_432 ::
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_432 :: T_Metric_396 -> T_IsPreorder_76
d_isPreorder_432 T_Metric_396
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.isProtoMetric
d_isProtoMetric_434 ::
  T_Metric_396 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_434 :: T_Metric_396 -> T_IsProtoMetric_30
d_isProtoMetric_434 T_Metric_396
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
         ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
            ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
               ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0)))))
-- Function.Metric.Nat.Bundles.Metric._.isQuasiSemiMetric
d_isQuasiSemiMetric_436 ::
  T_Metric_396 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_436 :: T_Metric_396 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_436 T_Metric_396
v0
  = (T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe
      T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
      ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
         ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0)))
-- Function.Metric.Nat.Bundles.Metric._.isSemiMetric
d_isSemiMetric_438 ::
  T_Metric_396 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_256
d_isSemiMetric_438 :: T_Metric_396 -> T_IsSemiMetric_256
d_isSemiMetric_438 T_Metric_396
v0
  = (T_IsGeneralMetric_340 -> T_IsSemiMetric_256)
-> AgdaAny -> T_IsSemiMetric_256
forall a b. a -> b
coe
      T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
      ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))
-- Function.Metric.Nat.Bundles.Metric._.nonNegative
d_nonNegative_440 ::
  T_Metric_396 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_440 :: T_Metric_396 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_440 T_Metric_396
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                  ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.refl
d_refl_442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_442 :: () -> () -> T_Metric_396 -> Integer -> T__'8804'__22
d_refl_442 ~()
v0 ~()
v1 T_Metric_396
v2 = T_Metric_396 -> Integer -> T__'8804'__22
du_refl_442 T_Metric_396
v2
du_refl_442 ::
  T_Metric_396 -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_442 :: T_Metric_396 -> Integer -> T__'8804'__22
du_refl_442 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.reflexive
d_reflexive_444 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_444 :: T_Metric_396
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_444 T_Metric_396
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                        ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.sym
d_sym_446 ::
  T_Metric_396 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_446 :: T_Metric_396 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_446 = T_Metric_396 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.trans
d_trans_448 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_448 :: T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_448 T_Metric_396
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                        ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.triangle
d_triangle_450 ::
  T_Metric_396 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_triangle_450 :: T_Metric_396 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
d_triangle_450 T_Metric_396
v0
  = (T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_triangle_352
      ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))
-- Function.Metric.Nat.Bundles.Metric._.≈-isEquivalence
d_'8776''45'isEquivalence_452 ::
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_452 :: T_Metric_396 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_452 T_Metric_396
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                  ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.≈⇒0
d_'8776''8658'0_454 ::
  T_Metric_396 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_454 :: T_Metric_396 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_454 = T_Metric_396 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.∼-resp-≈
d_'8764''45'resp'45''8776'_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_456 :: () -> () -> T_Metric_396 -> T_Σ_14
d_'8764''45'resp'45''8776'_456 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396 -> T_Σ_14
du_'8764''45'resp'45''8776'_456 T_Metric_396
v2
du_'8764''45'resp'45''8776'_456 ::
  T_Metric_396 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_456 :: T_Metric_396 -> T_Σ_14
du_'8764''45'resp'45''8776'_456 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_458 :: ()
-> ()
-> T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_458 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_458 T_Metric_396
v2
du_'8764''45'resp'691''45''8776'_458 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_458 :: T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_458 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_460 :: ()
-> ()
-> T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_460 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_460 T_Metric_396
v2
du_'8764''45'resp'737''45''8776'_460 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_460 :: T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_460 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.≲-resp-≈
d_'8818''45'resp'45''8776'_462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_462 :: () -> () -> T_Metric_396 -> T_Σ_14
d_'8818''45'resp'45''8776'_462 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396 -> T_Σ_14
du_'8818''45'resp'45''8776'_462 T_Metric_396
v2
du_'8818''45'resp'45''8776'_462 ::
  T_Metric_396 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_462 :: T_Metric_396 -> T_Σ_14
du_'8818''45'resp'45''8776'_462 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_464 :: ()
-> ()
-> T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_464 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_464 T_Metric_396
v2
du_'8818''45'resp'691''45''8776'_464 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_464 :: T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_464 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_466 :: ()
-> ()
-> T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_466 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_466 T_Metric_396
v2
du_'8818''45'resp'737''45''8776'_466 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_466 :: T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_466 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.isPartialEquivalence
d_isPartialEquivalence_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_470 :: () -> () -> T_Metric_396 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_470 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_470 T_Metric_396
v2
du_isPartialEquivalence_470 ::
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_470 :: T_Metric_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_470 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
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_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                        (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v5)))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.refl
d_refl_472 :: T_Metric_396 -> AgdaAny -> AgdaAny
d_refl_472 :: T_Metric_396 -> AgdaAny -> AgdaAny
d_refl_472 T_Metric_396
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.reflexive
d_reflexive_474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_474 :: ()
-> ()
-> T_Metric_396
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_474 ~()
v0 ~()
v1 T_Metric_396
v2 = T_Metric_396 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_474 T_Metric_396
v2
du_reflexive_474 ::
  T_Metric_396 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_474 :: T_Metric_396 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_474 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
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_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                          (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v5))
                       AgdaAny
v6)))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.sym
d_sym_476 ::
  T_Metric_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_476 :: T_Metric_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_476 T_Metric_396
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.trans
d_trans_478 ::
  T_Metric_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_478 :: T_Metric_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_478 T_Metric_396
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_Metric_396 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.Eq.isPartialEquivalence
d_isPartialEquivalence_482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_482 :: () -> () -> T_Metric_396 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_482 ~()
v0 ~()
v1 T_Metric_396
v2
  = T_Metric_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_482 T_Metric_396
v2
du_isPartialEquivalence_482 ::
  T_Metric_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_482 :: T_Metric_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_482 T_Metric_396
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsPreorder_76
v7
                            = 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
v6) 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
v7)))))))))
-- Function.Metric.Nat.Bundles.Metric._.Eq.refl
d_refl_484 ::
  T_Metric_396 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_484 :: T_Metric_396 -> Integer -> T__'8801'__12
d_refl_484 = T_Metric_396 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.reflexive
d_reflexive_486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_486 :: ()
-> ()
-> T_Metric_396
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_486 = ()
-> ()
-> T_Metric_396
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.sym
d_sym_488 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_488 :: T_Metric_396
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_488 = T_Metric_396
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.trans
d_trans_490 ::
  T_Metric_396 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_490 :: T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_490 = T_Metric_396
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric.semiMetric
d_semiMetric_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 -> T_SemiMetric_290
d_semiMetric_492 :: () -> () -> T_Metric_396 -> T_SemiMetric_290
d_semiMetric_492 ~()
v0 ~()
v1 T_Metric_396
v2 = T_Metric_396 -> T_SemiMetric_290
du_semiMetric_492 T_Metric_396
v2
du_semiMetric_492 :: T_Metric_396 -> T_SemiMetric_290
du_semiMetric_492 :: T_Metric_396 -> T_SemiMetric_290
du_semiMetric_492 T_Metric_396
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsSemiMetric_256 -> T_SemiMetric_290)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_256
-> T_SemiMetric_290
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_256 -> T_SemiMetric_290
C_constructor_390 (T_Metric_396 -> AgdaAny -> AgdaAny -> Integer
d_d_414 (T_Metric_396 -> T_Metric_396
forall a b. a -> b
coe T_Metric_396
v0))
      (T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
         ((T_Metric_396 -> T_IsGeneralMetric_340)
-> AgdaAny -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_Metric_396 -> T_IsGeneralMetric_340
d_isMetric_416 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0)))
-- Function.Metric.Nat.Bundles.Metric._.preMetric
d_preMetric_496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 -> T_PreMetric_98
d_preMetric_496 :: () -> () -> T_Metric_396 -> T_PreMetric_98
d_preMetric_496 ~()
v0 ~()
v1 T_Metric_396
v2 = T_Metric_396 -> T_PreMetric_98
du_preMetric_496 T_Metric_396
v2
du_preMetric_496 :: T_Metric_396 -> T_PreMetric_98
du_preMetric_496 :: T_Metric_396 -> T_PreMetric_98
du_preMetric_496 T_Metric_396
v0
  = let v1 :: AgdaAny
v1 = (T_Metric_396 -> T_SemiMetric_290) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_SemiMetric_290
du_semiMetric_492 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> T_PreMetric_98
forall a b. a -> b
coe ((T_QuasiSemiMetric_190 -> T_PreMetric_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 ((T_SemiMetric_290 -> T_QuasiSemiMetric_190) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Metric.Nat.Bundles.Metric._.protoMetric
d_protoMetric_498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 -> T_ProtoMetric_12
d_protoMetric_498 :: () -> () -> T_Metric_396 -> T_ProtoMetric_12
d_protoMetric_498 ~()
v0 ~()
v1 T_Metric_396
v2 = T_Metric_396 -> T_ProtoMetric_12
du_protoMetric_498 T_Metric_396
v2
du_protoMetric_498 :: T_Metric_396 -> T_ProtoMetric_12
du_protoMetric_498 :: T_Metric_396 -> T_ProtoMetric_12
du_protoMetric_498 T_Metric_396
v0
  = let v1 :: AgdaAny
v1 = (T_Metric_396 -> T_SemiMetric_290) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_SemiMetric_290
du_semiMetric_492 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_SemiMetric_290 -> T_QuasiSemiMetric_190) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_PreMetric_98 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_ProtoMetric_12
du_protoMetric_182 ((T_QuasiSemiMetric_190 -> T_PreMetric_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Metric.Nat.Bundles.Metric._.quasiSemiMetric
d_quasiSemiMetric_500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_396 -> T_QuasiSemiMetric_190
d_quasiSemiMetric_500 :: () -> () -> T_Metric_396 -> T_QuasiSemiMetric_190
d_quasiSemiMetric_500 ~()
v0 ~()
v1 T_Metric_396
v2 = T_Metric_396 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_500 T_Metric_396
v2
du_quasiSemiMetric_500 :: T_Metric_396 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_500 :: T_Metric_396 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_500 T_Metric_396
v0
  = (T_SemiMetric_290 -> T_QuasiSemiMetric_190)
-> AgdaAny -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 ((T_Metric_396 -> T_SemiMetric_290) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_396 -> T_SemiMetric_290
du_semiMetric_492 (T_Metric_396 -> AgdaAny
forall a b. a -> b
coe T_Metric_396
v0))
-- Function.Metric.Nat.Bundles.UltraMetric
d_UltraMetric_508 :: p -> p -> ()
d_UltraMetric_508 p
a0 p
a1 = ()
data T_UltraMetric_508
  = C_constructor_614 (AgdaAny -> AgdaAny -> Integer)
                      MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_340
-- Function.Metric.Nat.Bundles.UltraMetric.Carrier
d_Carrier_522 :: T_UltraMetric_508 -> ()
d_Carrier_522 :: T_UltraMetric_508 -> ()
d_Carrier_522 = T_UltraMetric_508 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._≈_
d__'8776'__524 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> ()
d__'8776'__524 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> ()
d__'8776'__524 = T_UltraMetric_508 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric.d
d_d_526 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> Integer
d_d_526 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> Integer
d_d_526 T_UltraMetric_508
v0
  = case T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0 of
      C_constructor_614 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_340
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_UltraMetric_508
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.UltraMetric.isUltraMetric
d_isUltraMetric_528 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_340
d_isUltraMetric_528 :: T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 T_UltraMetric_508
v0
  = case T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0 of
      C_constructor_614 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_340
v4 -> T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v4
      T_UltraMetric_508
_ -> T_IsGeneralMetric_340
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.UltraMetric._.0⇒≈
d_0'8658''8776'_532 ::
  T_UltraMetric_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_532 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_532 T_UltraMetric_508
v0
  = (T_IsQuasiSemiMetric_178
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
         ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
            ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))
-- Function.Metric.Nat.Bundles.UltraMetric._.antisym
d_antisym_534 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_534 :: T_UltraMetric_508
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_534 = T_UltraMetric_508
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.cong
d_cong_536 ::
  T_UltraMetric_508 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_536 :: T_UltraMetric_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_536 = T_UltraMetric_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.isEquivalence
d_isEquivalence_538 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_538 :: T_UltraMetric_508 -> T_IsEquivalence_28
d_isEquivalence_538 T_UltraMetric_508
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                        ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPartialOrder
d_isPartialOrder_540 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_540 :: T_UltraMetric_508 -> T_IsPartialOrder_248
d_isPartialOrder_540 T_UltraMetric_508
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                  ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPreMetric
d_isPreMetric_542 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_104
d_isPreMetric_542 :: T_UltraMetric_508 -> T_IsPreMetric_104
d_isPreMetric_542 T_UltraMetric_508
v0
  = (T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> T_IsPreMetric_104
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
      ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
         ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
            ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPreorder
d_isPreorder_544 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_544 :: T_UltraMetric_508 -> T_IsPreorder_76
d_isPreorder_544 T_UltraMetric_508
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isProtoMetric
d_isProtoMetric_546 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_546 :: T_UltraMetric_508 -> T_IsProtoMetric_30
d_isProtoMetric_546 T_UltraMetric_508
v0
  = (T_IsPreMetric_104 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
      ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
         ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
            ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
               ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0)))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_548 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_548 :: T_UltraMetric_508 -> T_IsQuasiSemiMetric_178
d_isQuasiSemiMetric_548 T_UltraMetric_508
v0
  = (T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe
      T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
      ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
         ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0)))
-- Function.Metric.Nat.Bundles.UltraMetric._.isSemiMetric
d_isSemiMetric_550 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_256
d_isSemiMetric_550 :: T_UltraMetric_508 -> T_IsSemiMetric_256
d_isSemiMetric_550 T_UltraMetric_508
v0
  = (T_IsGeneralMetric_340 -> T_IsSemiMetric_256)
-> AgdaAny -> T_IsSemiMetric_256
forall a b. a -> b
coe
      T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
      ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))
-- Function.Metric.Nat.Bundles.UltraMetric._.nonNegative
d_nonNegative_552 ::
  T_UltraMetric_508 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_552 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_552 T_UltraMetric_508
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                  ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.refl
d_refl_554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_554 :: () -> () -> T_UltraMetric_508 -> Integer -> T__'8804'__22
d_refl_554 ~()
v0 ~()
v1 T_UltraMetric_508
v2 = T_UltraMetric_508 -> Integer -> T__'8804'__22
du_refl_554 T_UltraMetric_508
v2
du_refl_554 ::
  T_UltraMetric_508 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_554 :: T_UltraMetric_508 -> Integer -> T__'8804'__22
du_refl_554 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.reflexive
d_reflexive_556 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_556 :: T_UltraMetric_508
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_556 T_UltraMetric_508
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                        ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.sym
d_sym_558 ::
  T_UltraMetric_508 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_558 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_558 = T_UltraMetric_508 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.trans
d_trans_560 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_560 :: T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_560 T_UltraMetric_508
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
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
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_104 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
               ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                  ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                     ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                        ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.triangle
d_triangle_562 ::
  T_UltraMetric_508 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_triangle_562 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
d_triangle_562 T_UltraMetric_508
v0
  = (T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsGeneralMetric_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_triangle_352
      ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))
-- Function.Metric.Nat.Bundles.UltraMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_564 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_'8776''45'isEquivalence_564 :: T_UltraMetric_508 -> T_IsEquivalence_28
d_'8776''45'isEquivalence_564 T_UltraMetric_508
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
         ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
            ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
               ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                  ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≈⇒0
d_'8776''8658'0_566 ::
  T_UltraMetric_508 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_566 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_566 = T_UltraMetric_508 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_568 :: () -> () -> T_UltraMetric_508 -> T_Σ_14
d_'8764''45'resp'45''8776'_568 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508 -> T_Σ_14
du_'8764''45'resp'45''8776'_568 T_UltraMetric_508
v2
du_'8764''45'resp'45''8776'_568 ::
  T_UltraMetric_508 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_568 :: T_UltraMetric_508 -> T_Σ_14
du_'8764''45'resp'45''8776'_568 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_570 :: ()
-> ()
-> T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_570 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_570 T_UltraMetric_508
v2
du_'8764''45'resp'691''45''8776'_570 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_570 :: T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_570 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_572 :: ()
-> ()
-> T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_572 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_572 T_UltraMetric_508
v2
du_'8764''45'resp'737''45''8776'_572 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_572 :: T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_572 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_574 :: () -> () -> T_UltraMetric_508 -> T_Σ_14
d_'8818''45'resp'45''8776'_574 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508 -> T_Σ_14
du_'8818''45'resp'45''8776'_574 T_UltraMetric_508
v2
du_'8818''45'resp'45''8776'_574 ::
  T_UltraMetric_508 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_574 :: T_UltraMetric_508 -> T_Σ_14
du_'8818''45'resp'45''8776'_574 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_576 :: ()
-> ()
-> T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_576 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_576 T_UltraMetric_508
v2
du_'8818''45'resp'691''45''8776'_576 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_576 :: T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_576 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_578 :: ()
-> ()
-> T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_578 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_578 T_UltraMetric_508
v2
du_'8818''45'resp'737''45''8776'_578 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_578 :: T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_578 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) 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
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_582 :: () -> () -> T_UltraMetric_508 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_582 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_582 T_UltraMetric_508
v2
du_isPartialEquivalence_582 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_582 :: T_UltraMetric_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_582 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
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_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                        (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v5)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.refl
d_refl_584 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny
d_refl_584 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny
d_refl_584 T_UltraMetric_508
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.reflexive
d_reflexive_586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_586 :: ()
-> ()
-> T_UltraMetric_508
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_586 ~()
v0 ~()
v1 T_UltraMetric_508
v2 = T_UltraMetric_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_586 T_UltraMetric_508
v2
du_reflexive_586 ::
  T_UltraMetric_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_586 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_586 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
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_IsProtoMetric_30 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsProtoMetric_30 -> T_IsEquivalence_28
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
                          (T_IsProtoMetric_30 -> AgdaAny
forall a b. a -> b
coe T_IsProtoMetric_30
v5))
                       AgdaAny
v6)))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.sym
d_sym_588 ::
  T_UltraMetric_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_588 :: T_UltraMetric_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_588 T_UltraMetric_508
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.trans
d_trans_590 ::
  T_UltraMetric_508 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_590 :: T_UltraMetric_508
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_590 T_UltraMetric_508
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
MAlonzo.Code.Function.Metric.Structures.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
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
            ((T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
               ((T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                  ((T_IsGeneralMetric_340 -> T_IsSemiMetric_256) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                     ((T_UltraMetric_508 -> T_IsGeneralMetric_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_594 :: () -> () -> T_UltraMetric_508 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_594 ~()
v0 ~()
v1 T_UltraMetric_508
v2
  = T_UltraMetric_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_594 T_UltraMetric_508
v2
du_isPartialEquivalence_594 ::
  T_UltraMetric_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_594 :: T_UltraMetric_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_594 T_UltraMetric_508
v0
  = let v1 :: T_IsGeneralMetric_340
v1 = T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_256
v2
             = T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
                 (T_IsGeneralMetric_340 -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_IsGeneralMetric_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_178
v3
                = T_IsSemiMetric_256 -> T_IsQuasiSemiMetric_178
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_264
                    (T_IsSemiMetric_256 -> T_IsSemiMetric_256
forall a b. a -> b
coe T_IsSemiMetric_256
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_104
v4
                   = T_IsQuasiSemiMetric_178 -> T_IsPreMetric_104
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_186
                       (T_IsQuasiSemiMetric_178 -> T_IsQuasiSemiMetric_178
forall a b. a -> b
coe T_IsQuasiSemiMetric_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_104 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_112
                          (T_IsPreMetric_104 -> T_IsPreMetric_104
forall a b. a -> b
coe T_IsPreMetric_104
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_248
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_248
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
                             (T_IsProtoMetric_30 -> T_IsProtoMetric_30
forall a b. a -> b
coe T_IsProtoMetric_30
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsPreorder_76
v7
                            = 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
v6) 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
v7)))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.refl
d_refl_596 ::
  T_UltraMetric_508 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_596 :: T_UltraMetric_508 -> Integer -> T__'8801'__12
d_refl_596 = T_UltraMetric_508 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.reflexive
d_reflexive_598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_598 :: ()
-> ()
-> T_UltraMetric_508
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_598 = ()
-> ()
-> T_UltraMetric_508
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.sym
d_sym_600 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_600 :: T_UltraMetric_508
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_600 = T_UltraMetric_508
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.trans
d_trans_602 ::
  T_UltraMetric_508 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_602 :: T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_602 = T_UltraMetric_508
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric.semiMetric
d_semiMetric_604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 -> T_SemiMetric_290
d_semiMetric_604 :: () -> () -> T_UltraMetric_508 -> T_SemiMetric_290
d_semiMetric_604 ~()
v0 ~()
v1 T_UltraMetric_508
v2 = T_UltraMetric_508 -> T_SemiMetric_290
du_semiMetric_604 T_UltraMetric_508
v2
du_semiMetric_604 :: T_UltraMetric_508 -> T_SemiMetric_290
du_semiMetric_604 :: T_UltraMetric_508 -> T_SemiMetric_290
du_semiMetric_604 T_UltraMetric_508
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsSemiMetric_256 -> T_SemiMetric_290)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_256
-> T_SemiMetric_290
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_256 -> T_SemiMetric_290
C_constructor_390 (T_UltraMetric_508 -> AgdaAny -> AgdaAny -> Integer
d_d_526 (T_UltraMetric_508 -> T_UltraMetric_508
forall a b. a -> b
coe T_UltraMetric_508
v0))
      (T_IsGeneralMetric_340 -> T_IsSemiMetric_256
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_350
         ((T_UltraMetric_508 -> T_IsGeneralMetric_340)
-> AgdaAny -> T_IsGeneralMetric_340
forall a b. a -> b
coe T_UltraMetric_508 -> T_IsGeneralMetric_340
d_isUltraMetric_528 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0)))
-- Function.Metric.Nat.Bundles.UltraMetric._.preMetric
d_preMetric_608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 -> T_PreMetric_98
d_preMetric_608 :: () -> () -> T_UltraMetric_508 -> T_PreMetric_98
d_preMetric_608 ~()
v0 ~()
v1 T_UltraMetric_508
v2 = T_UltraMetric_508 -> T_PreMetric_98
du_preMetric_608 T_UltraMetric_508
v2
du_preMetric_608 :: T_UltraMetric_508 -> T_PreMetric_98
du_preMetric_608 :: T_UltraMetric_508 -> T_PreMetric_98
du_preMetric_608 T_UltraMetric_508
v0
  = let v1 :: AgdaAny
v1 = (T_UltraMetric_508 -> T_SemiMetric_290) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_SemiMetric_290
du_semiMetric_604 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> T_PreMetric_98
forall a b. a -> b
coe ((T_QuasiSemiMetric_190 -> T_PreMetric_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 ((T_SemiMetric_290 -> T_QuasiSemiMetric_190) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Metric.Nat.Bundles.UltraMetric._.protoMetric
d_protoMetric_610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 -> T_ProtoMetric_12
d_protoMetric_610 :: () -> () -> T_UltraMetric_508 -> T_ProtoMetric_12
d_protoMetric_610 ~()
v0 ~()
v1 T_UltraMetric_508
v2 = T_UltraMetric_508 -> T_ProtoMetric_12
du_protoMetric_610 T_UltraMetric_508
v2
du_protoMetric_610 :: T_UltraMetric_508 -> T_ProtoMetric_12
du_protoMetric_610 :: T_UltraMetric_508 -> T_ProtoMetric_12
du_protoMetric_610 T_UltraMetric_508
v0
  = let v1 :: AgdaAny
v1 = (T_UltraMetric_508 -> T_SemiMetric_290) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_SemiMetric_290
du_semiMetric_604 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_SemiMetric_290 -> T_QuasiSemiMetric_190) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_PreMetric_98 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_98 -> T_ProtoMetric_12
du_protoMetric_182 ((T_QuasiSemiMetric_190 -> T_PreMetric_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_190 -> T_PreMetric_98
du_preMetric_278 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Metric.Nat.Bundles.UltraMetric._.quasiSemiMetric
d_quasiSemiMetric_612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_508 -> T_QuasiSemiMetric_190
d_quasiSemiMetric_612 :: () -> () -> T_UltraMetric_508 -> T_QuasiSemiMetric_190
d_quasiSemiMetric_612 ~()
v0 ~()
v1 T_UltraMetric_508
v2 = T_UltraMetric_508 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_612 T_UltraMetric_508
v2
du_quasiSemiMetric_612 ::
  T_UltraMetric_508 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_612 :: T_UltraMetric_508 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_612 T_UltraMetric_508
v0
  = (T_SemiMetric_290 -> T_QuasiSemiMetric_190)
-> AgdaAny -> T_QuasiSemiMetric_190
forall a b. a -> b
coe T_SemiMetric_290 -> T_QuasiSemiMetric_190
du_quasiSemiMetric_382 ((T_UltraMetric_508 -> T_SemiMetric_290) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508 -> T_SemiMetric_290
du_semiMetric_604 (T_UltraMetric_508 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_508
v0))