{-# 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_ProtoMetric'46'constructor_193 (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_ProtoMetric'46'constructor_193 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_ProtoMetric'46'constructor_193 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'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_36 :: T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
d_antisym_36 = T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> 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_26
d_isEquivalence_40 :: T_ProtoMetric_12 -> T_IsEquivalence_26
d_isEquivalence_40 T_ProtoMetric_12
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_162
d_isPartialOrder_42 :: T_ProtoMetric_12 -> T_IsPartialOrder_162
d_isPartialOrder_42 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
d_isPreorder_44 :: T_ProtoMetric_12 -> T_IsPreorder_70
d_isPreorder_44 T_ProtoMetric_12
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
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'__18
d_nonNegative_46 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8804'__18
d_nonNegative_46 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
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'__18
d_refl_48 :: () -> () -> T_ProtoMetric_12 -> Integer -> T__'8804'__18
d_refl_48 ~()
v0 ~()
v1 T_ProtoMetric_12
v2 = T_ProtoMetric_12 -> Integer -> T__'8804'__18
du_refl_48 T_ProtoMetric_12
v2
du_refl_48 ::
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_refl_48 :: T_ProtoMetric_12 -> Integer -> T__'8804'__18
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'__18
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.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'__18
d_reflexive_50 :: T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
d_reflexive_50 T_ProtoMetric_12
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
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'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_trans_52 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
d_trans_52 T_ProtoMetric_12
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_26
d_'8776''45'isEquivalence_54 :: T_ProtoMetric_12 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_54 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
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_162
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.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'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'691''45''8776'_58 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
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'__18
-> T__'8804'__18
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'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'691''45''8776'_58 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
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'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.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'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'737''45''8776'_60 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
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'__18
-> T__'8804'__18
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'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'737''45''8776'_60 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
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'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_64 ::
  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_64 :: () -> () -> T_ProtoMetric_12 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_64 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_64 T_ProtoMetric_12
v2
du_isPartialEquivalence_64 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_64 :: T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_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 -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsEquivalence_26
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_66 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny
d_refl_66 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny
d_refl_66 T_ProtoMetric_12
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
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_68 ::
  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_68 :: ()
-> ()
-> T_ProtoMetric_12
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_68 ~()
v0 ~()
v1 T_ProtoMetric_12
v2 = T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_68 T_ProtoMetric_12
v2
du_reflexive_68 ::
  T_ProtoMetric_12 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_68 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_68 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_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsProtoMetric_30 -> T_IsEquivalence_26
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_70 ::
  T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_70 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_70 T_ProtoMetric_12
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
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_72 ::
  T_ProtoMetric_12 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_72 :: T_ProtoMetric_12
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_72 T_ProtoMetric_12
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
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_76 ::
  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_76 :: () -> () -> T_ProtoMetric_12 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_76 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_76 T_ProtoMetric_12
v2
du_isPartialEquivalence_76 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_76 :: T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_76 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_162
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.refl
d_refl_78 ::
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_78 :: T_ProtoMetric_12 -> Integer -> T__'8801'__12
d_refl_78 = T_ProtoMetric_12 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.reflexive
d_reflexive_80 ::
  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_80 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_80 = ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.sym
d_sym_82 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_82 :: T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_82 = T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.trans
d_trans_84 ::
  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_84 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_84 = 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_90 :: p -> p -> ()
d_PreMetric_90 p
a0 p
a1 = ()
data T_PreMetric_90
  = C_PreMetric'46'constructor_1523 (AgdaAny -> AgdaAny -> Integer)
                                    MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_96
-- Function.Metric.Nat.Bundles.PreMetric.Carrier
d_Carrier_104 :: T_PreMetric_90 -> ()
d_Carrier_104 :: T_PreMetric_90 -> ()
d_Carrier_104 = T_PreMetric_90 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._≈_
d__'8776'__106 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> ()
d__'8776'__106 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> ()
d__'8776'__106 = T_PreMetric_90 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric.d
d_d_108 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> Integer
d_d_108 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> Integer
d_d_108 T_PreMetric_90
v0
  = case T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0 of
      C_PreMetric'46'constructor_1523 AgdaAny -> AgdaAny -> Integer
v3 T_IsPreMetric_96
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_PreMetric_90
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.PreMetric.isPreMetric
d_isPreMetric_110 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_96
d_isPreMetric_110 :: T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 T_PreMetric_90
v0
  = case T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0 of
      C_PreMetric'46'constructor_1523 AgdaAny -> AgdaAny -> Integer
v3 T_IsPreMetric_96
v4 -> T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4
      T_PreMetric_90
_ -> T_IsPreMetric_96
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.PreMetric._.antisym
d_antisym_114 ::
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_114 :: T_PreMetric_90
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
d_antisym_114 = T_PreMetric_90
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.cong
d_cong_116 ::
  T_PreMetric_90 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_116 :: T_PreMetric_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_116 = T_PreMetric_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.isEquivalence
d_isEquivalence_118 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_118 :: T_PreMetric_90 -> T_IsEquivalence_26
d_isEquivalence_118 T_PreMetric_90
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.isPartialOrder
d_isPartialOrder_120 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_120 :: T_PreMetric_90 -> T_IsPartialOrder_162
d_isPartialOrder_120 T_PreMetric_90
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.isPreorder
d_isPreorder_122 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_122 :: T_PreMetric_90 -> T_IsPreorder_70
d_isPreorder_122 T_PreMetric_90
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.isProtoMetric
d_isProtoMetric_124 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_124 :: T_PreMetric_90 -> T_IsProtoMetric_30
d_isProtoMetric_124 T_PreMetric_90
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
      ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0))
-- Function.Metric.Nat.Bundles.PreMetric._.nonNegative
d_nonNegative_126 ::
  T_PreMetric_90 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_nonNegative_126 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> T__'8804'__18
d_nonNegative_126 T_PreMetric_90
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.refl
d_refl_128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_refl_128 :: () -> () -> T_PreMetric_90 -> Integer -> T__'8804'__18
d_refl_128 ~()
v0 ~()
v1 T_PreMetric_90
v2 = T_PreMetric_90 -> Integer -> T__'8804'__18
du_refl_128 T_PreMetric_90
v2
du_refl_128 ::
  T_PreMetric_90 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_refl_128 :: T_PreMetric_90 -> Integer -> T__'8804'__18
du_refl_128 T_PreMetric_90
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0) in
    AgdaAny -> Integer -> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.reflexive
d_reflexive_130 ::
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_reflexive_130 :: T_PreMetric_90
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
d_reflexive_130 T_PreMetric_90
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.trans
d_trans_132 ::
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_trans_132 :: T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
d_trans_132 T_PreMetric_90
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_134 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_134 :: T_PreMetric_90 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_134 T_PreMetric_90
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.≈⇒0
d_'8776''8658'0_136 ::
  T_PreMetric_90 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_136 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_136 = T_PreMetric_90 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_138 :: () -> () -> T_PreMetric_90 -> T_Σ_14
d_'8764''45'resp'45''8776'_138 ~()
v0 ~()
v1 T_PreMetric_90
v2
  = T_PreMetric_90 -> T_Σ_14
du_'8764''45'resp'45''8776'_138 T_PreMetric_90
v2
du_'8764''45'resp'45''8776'_138 ::
  T_PreMetric_90 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_138 :: T_PreMetric_90 -> T_Σ_14
du_'8764''45'resp'45''8776'_138 T_PreMetric_90
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'691''45''8776'_140 :: ()
-> ()
-> T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'691''45''8776'_140 ~()
v0 ~()
v1 T_PreMetric_90
v2
  = T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_140 T_PreMetric_90
v2
du_'8764''45'resp'691''45''8776'_140 ::
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'691''45''8776'_140 :: T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_140 T_PreMetric_90
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'737''45''8776'_142 :: ()
-> ()
-> T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'737''45''8776'_142 ~()
v0 ~()
v1 T_PreMetric_90
v2
  = T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_142 T_PreMetric_90
v2
du_'8764''45'resp'737''45''8776'_142 ::
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'737''45''8776'_142 :: T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_142 T_PreMetric_90
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_146 :: () -> () -> T_PreMetric_90 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_146 ~()
v0 ~()
v1 T_PreMetric_90
v2
  = T_PreMetric_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_146 T_PreMetric_90
v2
du_isPartialEquivalence_146 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_146 :: T_PreMetric_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_146 T_PreMetric_90
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsEquivalence_26
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_148 :: T_PreMetric_90 -> AgdaAny -> AgdaAny
d_refl_148 :: T_PreMetric_90 -> AgdaAny -> AgdaAny
d_refl_148 T_PreMetric_90
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.reflexive
d_reflexive_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_150 :: ()
-> ()
-> T_PreMetric_90
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_150 ~()
v0 ~()
v1 T_PreMetric_90
v2 = T_PreMetric_90 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_150 T_PreMetric_90
v2
du_reflexive_150 ::
  T_PreMetric_90 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_150 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_150 T_PreMetric_90
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsProtoMetric_30 -> T_IsEquivalence_26
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_152 ::
  T_PreMetric_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_152 :: T_PreMetric_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_152 T_PreMetric_90
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.trans
d_trans_154 ::
  T_PreMetric_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_154 :: T_PreMetric_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_154 T_PreMetric_90
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_158 :: () -> () -> T_PreMetric_90 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_158 ~()
v0 ~()
v1 T_PreMetric_90
v2
  = T_PreMetric_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_158 T_PreMetric_90
v2
du_isPartialEquivalence_158 ::
  T_PreMetric_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_158 :: T_PreMetric_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_158 T_PreMetric_90
v0
  = let v1 :: T_IsPreMetric_96
v1 = T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                 (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.refl
d_refl_160 ::
  T_PreMetric_90 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_160 :: T_PreMetric_90 -> Integer -> T__'8801'__12
d_refl_160 = T_PreMetric_90 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.reflexive
d_reflexive_162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_162 :: ()
-> ()
-> T_PreMetric_90
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_162 = ()
-> ()
-> T_PreMetric_90
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.sym
d_sym_164 ::
  T_PreMetric_90 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_164 :: T_PreMetric_90
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_164 = T_PreMetric_90
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.trans
d_trans_166 ::
  T_PreMetric_90 ->
  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_166 :: T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_166 = T_PreMetric_90
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric.protoMetric
d_protoMetric_168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_90 -> T_ProtoMetric_12
d_protoMetric_168 :: () -> () -> T_PreMetric_90 -> T_ProtoMetric_12
d_protoMetric_168 ~()
v0 ~()
v1 T_PreMetric_90
v2 = T_PreMetric_90 -> T_ProtoMetric_12
du_protoMetric_168 T_PreMetric_90
v2
du_protoMetric_168 :: T_PreMetric_90 -> T_ProtoMetric_12
du_protoMetric_168 :: T_PreMetric_90 -> T_ProtoMetric_12
du_protoMetric_168 T_PreMetric_90
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_ProtoMetric'46'constructor_193 (T_PreMetric_90 -> AgdaAny -> AgdaAny -> Integer
d_d_108 (T_PreMetric_90 -> T_PreMetric_90
forall a b. a -> b
coe T_PreMetric_90
v0))
      (T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_PreMetric_90 -> T_IsPreMetric_96) -> AgdaAny -> T_IsPreMetric_96
forall a b. a -> b
coe T_PreMetric_90 -> T_IsPreMetric_96
d_isPreMetric_110 (T_PreMetric_90 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric
d_QuasiSemiMetric_174 :: p -> p -> ()
d_QuasiSemiMetric_174 p
a0 p
a1 = ()
data T_QuasiSemiMetric_174
  = C_QuasiSemiMetric'46'constructor_3043 (AgdaAny ->
                                           AgdaAny -> Integer)
                                          MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_162
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.Carrier
d_Carrier_188 :: T_QuasiSemiMetric_174 -> ()
d_Carrier_188 :: T_QuasiSemiMetric_174 -> ()
d_Carrier_188 = T_QuasiSemiMetric_174 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._≈_
d__'8776'__190 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> ()
d__'8776'__190 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> ()
d__'8776'__190 = T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.d
d_d_192 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> Integer
d_d_192 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> Integer
d_d_192 T_QuasiSemiMetric_174
v0
  = case T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0 of
      C_QuasiSemiMetric'46'constructor_3043 AgdaAny -> AgdaAny -> Integer
v3 T_IsQuasiSemiMetric_162
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_QuasiSemiMetric_174
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.isQuasiSemiMetric
d_isQuasiSemiMetric_194 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 :: T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 T_QuasiSemiMetric_174
v0
  = case T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0 of
      C_QuasiSemiMetric'46'constructor_3043 AgdaAny -> AgdaAny -> Integer
v3 T_IsQuasiSemiMetric_162
v4 -> T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v4
      T_QuasiSemiMetric_174
_ -> T_IsQuasiSemiMetric_162
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.0⇒≈
d_0'8658''8776'_198 ::
  T_QuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_198 :: T_QuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_198 T_QuasiSemiMetric_174
v0
  = (T_IsQuasiSemiMetric_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_172
      ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.antisym
d_antisym_200 ::
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_200 :: T_QuasiSemiMetric_174
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
d_antisym_200 = T_QuasiSemiMetric_174
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.cong
d_cong_202 ::
  T_QuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_202 :: T_QuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_202 = T_QuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isEquivalence
d_isEquivalence_204 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_204 :: T_QuasiSemiMetric_174 -> T_IsEquivalence_26
d_isEquivalence_204 T_QuasiSemiMetric_174
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPartialOrder
d_isPartialOrder_206 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_206 :: T_QuasiSemiMetric_174 -> T_IsPartialOrder_162
d_isPartialOrder_206 T_QuasiSemiMetric_174
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPreMetric
d_isPreMetric_208 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_96
d_isPreMetric_208 :: T_QuasiSemiMetric_174 -> T_IsPreMetric_96
d_isPreMetric_208 T_QuasiSemiMetric_174
v0
  = (T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96)
-> AgdaAny -> T_IsPreMetric_96
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
      ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPreorder
d_isPreorder_210 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_210 :: T_QuasiSemiMetric_174 -> T_IsPreorder_70
d_isPreorder_210 T_QuasiSemiMetric_174
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isProtoMetric
d_isProtoMetric_212 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_212 :: T_QuasiSemiMetric_174 -> T_IsProtoMetric_30
d_isProtoMetric_212 T_QuasiSemiMetric_174
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
         ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.nonNegative
d_nonNegative_214 ::
  T_QuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_nonNegative_214 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> T__'8804'__18
d_nonNegative_214 T_QuasiSemiMetric_174
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.refl
d_refl_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_refl_216 :: () -> () -> T_QuasiSemiMetric_174 -> Integer -> T__'8804'__18
d_refl_216 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2 = T_QuasiSemiMetric_174 -> Integer -> T__'8804'__18
du_refl_216 T_QuasiSemiMetric_174
v2
du_refl_216 ::
  T_QuasiSemiMetric_174 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_refl_216 :: T_QuasiSemiMetric_174 -> Integer -> T__'8804'__18
du_refl_216 T_QuasiSemiMetric_174
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0) in
    AgdaAny -> Integer -> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2
             = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                    (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.reflexive
d_reflexive_218 ::
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_reflexive_218 :: T_QuasiSemiMetric_174
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
d_reflexive_218 T_QuasiSemiMetric_174
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.trans
d_trans_220 ::
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_trans_220 :: T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
d_trans_220 T_QuasiSemiMetric_174
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_222 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_222 :: T_QuasiSemiMetric_174 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_222 T_QuasiSemiMetric_174
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≈⇒0
d_'8776''8658'0_224 ::
  T_QuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_224 :: T_QuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_224 = T_QuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_226 :: () -> () -> T_QuasiSemiMetric_174 -> T_Σ_14
d_'8764''45'resp'45''8776'_226 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2
  = T_QuasiSemiMetric_174 -> T_Σ_14
du_'8764''45'resp'45''8776'_226 T_QuasiSemiMetric_174
v2
du_'8764''45'resp'45''8776'_226 ::
  T_QuasiSemiMetric_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_226 :: T_QuasiSemiMetric_174 -> T_Σ_14
du_'8764''45'resp'45''8776'_226 T_QuasiSemiMetric_174
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2
             = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                    (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'691''45''8776'_228 :: ()
-> ()
-> T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'691''45''8776'_228 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2
  = T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_228 T_QuasiSemiMetric_174
v2
du_'8764''45'resp'691''45''8776'_228 ::
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'691''45''8776'_228 :: T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_228 T_QuasiSemiMetric_174
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2
             = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                    (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'737''45''8776'_230 :: ()
-> ()
-> T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'737''45''8776'_230 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2
  = T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_230 T_QuasiSemiMetric_174
v2
du_'8764''45'resp'737''45''8776'_230 ::
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'737''45''8776'_230 :: T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_230 T_QuasiSemiMetric_174
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2
             = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                    (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_234 :: () -> () -> T_QuasiSemiMetric_174 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_234 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2
  = T_QuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_234 T_QuasiSemiMetric_174
v2
du_isPartialEquivalence_234 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_234 :: T_QuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_234 T_QuasiSemiMetric_174
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2
             = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                    (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsProtoMetric_30 -> T_IsEquivalence_26
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_236 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny
d_refl_236 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny
d_refl_236 T_QuasiSemiMetric_174
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.reflexive
d_reflexive_238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_238 :: ()
-> ()
-> T_QuasiSemiMetric_174
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_238 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2 = T_QuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_238 T_QuasiSemiMetric_174
v2
du_reflexive_238 ::
  T_QuasiSemiMetric_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_238 :: T_QuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_238 T_QuasiSemiMetric_174
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2
             = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                    (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsProtoMetric_30 -> T_IsEquivalence_26
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_240 ::
  T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_240 :: T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_240 T_QuasiSemiMetric_174
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.trans
d_trans_242 ::
  T_QuasiSemiMetric_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_242 :: T_QuasiSemiMetric_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_242 T_QuasiSemiMetric_174
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_246 :: () -> () -> T_QuasiSemiMetric_174 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_246 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2
  = T_QuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_246 T_QuasiSemiMetric_174
v2
du_isPartialEquivalence_246 ::
  T_QuasiSemiMetric_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_246 :: T_QuasiSemiMetric_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_246 T_QuasiSemiMetric_174
v0
  = let v1 :: T_IsQuasiSemiMetric_162
v1 = T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_96
v2
             = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                 (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                    (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
v5
                      = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                          (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5)))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.refl
d_refl_248 ::
  T_QuasiSemiMetric_174 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_248 :: T_QuasiSemiMetric_174 -> Integer -> T__'8801'__12
d_refl_248 = T_QuasiSemiMetric_174 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.reflexive
d_reflexive_250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_250 :: ()
-> ()
-> T_QuasiSemiMetric_174
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_250 = ()
-> ()
-> T_QuasiSemiMetric_174
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.sym
d_sym_252 ::
  T_QuasiSemiMetric_174 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_252 :: T_QuasiSemiMetric_174
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_252 = T_QuasiSemiMetric_174
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.trans
d_trans_254 ::
  T_QuasiSemiMetric_174 ->
  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_254 :: T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_254 = T_QuasiSemiMetric_174
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.preMetric
d_preMetric_256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 -> T_PreMetric_90
d_preMetric_256 :: () -> () -> T_QuasiSemiMetric_174 -> T_PreMetric_90
d_preMetric_256 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2 = T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 T_QuasiSemiMetric_174
v2
du_preMetric_256 :: T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 :: T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 T_QuasiSemiMetric_174
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsPreMetric_96 -> T_PreMetric_90)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsPreMetric_96
-> T_PreMetric_90
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsPreMetric_96 -> T_PreMetric_90
C_PreMetric'46'constructor_1523 (T_QuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> Integer
d_d_192 (T_QuasiSemiMetric_174 -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))
      (T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
         ((T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_194 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.protoMetric
d_protoMetric_260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_174 -> T_ProtoMetric_12
d_protoMetric_260 :: () -> () -> T_QuasiSemiMetric_174 -> T_ProtoMetric_12
d_protoMetric_260 ~()
v0 ~()
v1 T_QuasiSemiMetric_174
v2 = T_QuasiSemiMetric_174 -> T_ProtoMetric_12
du_protoMetric_260 T_QuasiSemiMetric_174
v2
du_protoMetric_260 :: T_QuasiSemiMetric_174 -> T_ProtoMetric_12
du_protoMetric_260 :: T_QuasiSemiMetric_174 -> T_ProtoMetric_12
du_protoMetric_260 T_QuasiSemiMetric_174
v0
  = (T_PreMetric_90 -> T_ProtoMetric_12) -> AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe T_PreMetric_90 -> T_ProtoMetric_12
du_protoMetric_168 ((T_QuasiSemiMetric_174 -> T_PreMetric_90) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 (T_QuasiSemiMetric_174 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174
v0))
-- Function.Metric.Nat.Bundles.SemiMetric
d_SemiMetric_266 :: p -> p -> ()
d_SemiMetric_266 p
a0 p
a1 = ()
data T_SemiMetric_266
  = C_SemiMetric'46'constructor_4673 (AgdaAny -> AgdaAny -> Integer)
                                     MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_232
-- Function.Metric.Nat.Bundles.SemiMetric.Carrier
d_Carrier_280 :: T_SemiMetric_266 -> ()
d_Carrier_280 :: T_SemiMetric_266 -> ()
d_Carrier_280 = T_SemiMetric_266 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._≈_
d__'8776'__282 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> ()
d__'8776'__282 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> ()
d__'8776'__282 = T_SemiMetric_266 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric.d
d_d_284 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> Integer
d_d_284 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> Integer
d_d_284 T_SemiMetric_266
v0
  = case T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0 of
      C_SemiMetric'46'constructor_4673 AgdaAny -> AgdaAny -> Integer
v3 T_IsSemiMetric_232
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_SemiMetric_266
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.SemiMetric.isSemiMetric
d_isSemiMetric_286 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_232
d_isSemiMetric_286 :: T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 T_SemiMetric_266
v0
  = case T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0 of
      C_SemiMetric'46'constructor_4673 AgdaAny -> AgdaAny -> Integer
v3 T_IsSemiMetric_232
v4 -> T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v4
      T_SemiMetric_266
_ -> T_IsSemiMetric_232
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.SemiMetric._.0⇒≈
d_0'8658''8776'_290 ::
  T_SemiMetric_266 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_290 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_290 T_SemiMetric_266
v0
  = (T_IsQuasiSemiMetric_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_172
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
         ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.antisym
d_antisym_292 ::
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_292 :: T_SemiMetric_266
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
d_antisym_292 = T_SemiMetric_266
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.cong
d_cong_294 ::
  T_SemiMetric_266 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_294 :: T_SemiMetric_266
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_294 = T_SemiMetric_266
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.isEquivalence
d_isEquivalence_296 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_296 :: T_SemiMetric_266 -> T_IsEquivalence_26
d_isEquivalence_296 T_SemiMetric_266
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPartialOrder
d_isPartialOrder_298 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_298 :: T_SemiMetric_266 -> T_IsPartialOrder_162
d_isPartialOrder_298 T_SemiMetric_266
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPreMetric
d_isPreMetric_300 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_96
d_isPreMetric_300 :: T_SemiMetric_266 -> T_IsPreMetric_96
d_isPreMetric_300 T_SemiMetric_266
v0
  = (T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96)
-> AgdaAny -> T_IsPreMetric_96
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
         ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPreorder
d_isPreorder_302 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_302 :: T_SemiMetric_266 -> T_IsPreorder_70
d_isPreorder_302 T_SemiMetric_266
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isProtoMetric
d_isProtoMetric_304 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_304 :: T_SemiMetric_266 -> T_IsProtoMetric_30
d_isProtoMetric_304 T_SemiMetric_266
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
         ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
            ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_306 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_306 :: T_SemiMetric_266 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_306 T_SemiMetric_266
v0
  = (T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe
      T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
      ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0))
-- Function.Metric.Nat.Bundles.SemiMetric._.nonNegative
d_nonNegative_308 ::
  T_SemiMetric_266 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_nonNegative_308 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> T__'8804'__18
d_nonNegative_308 T_SemiMetric_266
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.refl
d_refl_310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_refl_310 :: () -> () -> T_SemiMetric_266 -> Integer -> T__'8804'__18
d_refl_310 ~()
v0 ~()
v1 T_SemiMetric_266
v2 = T_SemiMetric_266 -> Integer -> T__'8804'__18
du_refl_310 T_SemiMetric_266
v2
du_refl_310 ::
  T_SemiMetric_266 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_refl_310 :: T_SemiMetric_266 -> Integer -> T__'8804'__18
du_refl_310 T_SemiMetric_266
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny -> Integer -> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2
             = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3
                = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                    (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                       (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.reflexive
d_reflexive_312 ::
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_reflexive_312 :: T_SemiMetric_266
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
d_reflexive_312 T_SemiMetric_266
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.sym
d_sym_314 ::
  T_SemiMetric_266 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_314 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_314 = T_SemiMetric_266 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.trans
d_trans_316 ::
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_trans_316 :: T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
d_trans_316 T_SemiMetric_266
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_318 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_318 :: T_SemiMetric_266 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_318 T_SemiMetric_266
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≈⇒0
d_'8776''8658'0_320 ::
  T_SemiMetric_266 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_320 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_320 = T_SemiMetric_266 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_322 :: () -> () -> T_SemiMetric_266 -> T_Σ_14
d_'8764''45'resp'45''8776'_322 ~()
v0 ~()
v1 T_SemiMetric_266
v2
  = T_SemiMetric_266 -> T_Σ_14
du_'8764''45'resp'45''8776'_322 T_SemiMetric_266
v2
du_'8764''45'resp'45''8776'_322 ::
  T_SemiMetric_266 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_322 :: T_SemiMetric_266 -> T_Σ_14
du_'8764''45'resp'45''8776'_322 T_SemiMetric_266
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2
             = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3
                = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                    (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                       (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'691''45''8776'_324 :: ()
-> ()
-> T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'691''45''8776'_324 ~()
v0 ~()
v1 T_SemiMetric_266
v2
  = T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_324 T_SemiMetric_266
v2
du_'8764''45'resp'691''45''8776'_324 ::
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'691''45''8776'_324 :: T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_324 T_SemiMetric_266
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2
             = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3
                = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                    (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                       (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'737''45''8776'_326 :: ()
-> ()
-> T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'737''45''8776'_326 ~()
v0 ~()
v1 T_SemiMetric_266
v2
  = T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_326 T_SemiMetric_266
v2
du_'8764''45'resp'737''45''8776'_326 ::
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'737''45''8776'_326 :: T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_326 T_SemiMetric_266
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2
             = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3
                = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                    (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                       (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_330 :: () -> () -> T_SemiMetric_266 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_330 ~()
v0 ~()
v1 T_SemiMetric_266
v2
  = T_SemiMetric_266 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_330 T_SemiMetric_266
v2
du_isPartialEquivalence_330 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_330 :: T_SemiMetric_266 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_330 T_SemiMetric_266
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2
             = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3
                = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                    (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                       (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsProtoMetric_30 -> T_IsEquivalence_26
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_332 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny
d_refl_332 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny
d_refl_332 T_SemiMetric_266
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.reflexive
d_reflexive_334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_334 :: ()
-> ()
-> T_SemiMetric_266
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_334 ~()
v0 ~()
v1 T_SemiMetric_266
v2 = T_SemiMetric_266 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_334 T_SemiMetric_266
v2
du_reflexive_334 ::
  T_SemiMetric_266 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_334 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_334 T_SemiMetric_266
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2
             = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3
                = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                    (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                       (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsProtoMetric_30 -> T_IsEquivalence_26
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_336 ::
  T_SemiMetric_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_336 :: T_SemiMetric_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_336 T_SemiMetric_266
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.trans
d_trans_338 ::
  T_SemiMetric_266 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_338 :: T_SemiMetric_266
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_338 T_SemiMetric_266
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_SemiMetric_266 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_342 :: () -> () -> T_SemiMetric_266 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_342 ~()
v0 ~()
v1 T_SemiMetric_266
v2
  = T_SemiMetric_266 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_342 T_SemiMetric_266
v2
du_isPartialEquivalence_342 ::
  T_SemiMetric_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_342 :: T_SemiMetric_266 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_342 T_SemiMetric_266
v0
  = let v1 :: T_IsSemiMetric_232
v1 = T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_162
v2
             = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                 (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_96
v3
                = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                    (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                       (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
v6
                         = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                             (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.refl
d_refl_344 ::
  T_SemiMetric_266 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_344 :: T_SemiMetric_266 -> Integer -> T__'8801'__12
d_refl_344 = T_SemiMetric_266 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.reflexive
d_reflexive_346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_346 :: ()
-> ()
-> T_SemiMetric_266
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_346 = ()
-> ()
-> T_SemiMetric_266
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.sym
d_sym_348 ::
  T_SemiMetric_266 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_348 :: T_SemiMetric_266
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_348 = T_SemiMetric_266
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.trans
d_trans_350 ::
  T_SemiMetric_266 ->
  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_350 :: T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_350 = T_SemiMetric_266
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric.quasiSemiMetric
d_quasiSemiMetric_352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 -> T_QuasiSemiMetric_174
d_quasiSemiMetric_352 :: () -> () -> T_SemiMetric_266 -> T_QuasiSemiMetric_174
d_quasiSemiMetric_352 ~()
v0 ~()
v1 T_SemiMetric_266
v2 = T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 T_SemiMetric_266
v2
du_quasiSemiMetric_352 :: T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 :: T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 T_SemiMetric_266
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsQuasiSemiMetric_162 -> T_QuasiSemiMetric_174)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsQuasiSemiMetric_162
-> T_QuasiSemiMetric_174
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsQuasiSemiMetric_162 -> T_QuasiSemiMetric_174
C_QuasiSemiMetric'46'constructor_3043 (T_SemiMetric_266 -> AgdaAny -> AgdaAny -> Integer
d_d_284 (T_SemiMetric_266 -> T_SemiMetric_266
forall a b. a -> b
coe T_SemiMetric_266
v0))
      (T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
         ((T_SemiMetric_266 -> T_IsSemiMetric_232)
-> AgdaAny -> T_IsSemiMetric_232
forall a b. a -> b
coe T_SemiMetric_266 -> T_IsSemiMetric_232
d_isSemiMetric_286 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.preMetric
d_preMetric_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 -> T_PreMetric_90
d_preMetric_356 :: () -> () -> T_SemiMetric_266 -> T_PreMetric_90
d_preMetric_356 ~()
v0 ~()
v1 T_SemiMetric_266
v2 = T_SemiMetric_266 -> T_PreMetric_90
du_preMetric_356 T_SemiMetric_266
v2
du_preMetric_356 :: T_SemiMetric_266 -> T_PreMetric_90
du_preMetric_356 :: T_SemiMetric_266 -> T_PreMetric_90
du_preMetric_356 T_SemiMetric_266
v0
  = (T_QuasiSemiMetric_174 -> T_PreMetric_90)
-> AgdaAny -> T_PreMetric_90
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 ((T_SemiMetric_266 -> T_QuasiSemiMetric_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0))
-- Function.Metric.Nat.Bundles.SemiMetric._.protoMetric
d_protoMetric_358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_266 -> T_ProtoMetric_12
d_protoMetric_358 :: () -> () -> T_SemiMetric_266 -> T_ProtoMetric_12
d_protoMetric_358 ~()
v0 ~()
v1 T_SemiMetric_266
v2 = T_SemiMetric_266 -> T_ProtoMetric_12
du_protoMetric_358 T_SemiMetric_266
v2
du_protoMetric_358 :: T_SemiMetric_266 -> T_ProtoMetric_12
du_protoMetric_358 :: T_SemiMetric_266 -> T_ProtoMetric_12
du_protoMetric_358 T_SemiMetric_266
v0
  = let v1 :: t
v1 = (T_SemiMetric_266 -> T_QuasiSemiMetric_174) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 (T_SemiMetric_266 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe ((T_PreMetric_90 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_ProtoMetric_12
du_protoMetric_168 ((T_QuasiSemiMetric_174 -> T_PreMetric_90) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Metric.Nat.Bundles.Metric
d_Metric_364 :: p -> p -> ()
d_Metric_364 p
a0 p
a1 = ()
data T_Metric_364
  = C_Metric'46'constructor_6373 (AgdaAny -> AgdaAny -> Integer)
                                 MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_308
-- Function.Metric.Nat.Bundles.Metric.Carrier
d_Carrier_378 :: T_Metric_364 -> ()
d_Carrier_378 :: T_Metric_364 -> ()
d_Carrier_378 = T_Metric_364 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._≈_
d__'8776'__380 :: T_Metric_364 -> AgdaAny -> AgdaAny -> ()
d__'8776'__380 :: T_Metric_364 -> AgdaAny -> AgdaAny -> ()
d__'8776'__380 = T_Metric_364 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric.d
d_d_382 :: T_Metric_364 -> AgdaAny -> AgdaAny -> Integer
d_d_382 :: T_Metric_364 -> AgdaAny -> AgdaAny -> Integer
d_d_382 T_Metric_364
v0
  = case T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0 of
      C_Metric'46'constructor_6373 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_308
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_Metric_364
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.Metric.isMetric
d_isMetric_384 ::
  T_Metric_364 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_308
d_isMetric_384 :: T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 T_Metric_364
v0
  = case T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0 of
      C_Metric'46'constructor_6373 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_308
v4 -> T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v4
      T_Metric_364
_ -> T_IsGeneralMetric_308
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.Metric._.0⇒≈
d_0'8658''8776'_388 ::
  T_Metric_364 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_388 :: T_Metric_364 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_388 T_Metric_364
v0
  = (T_IsQuasiSemiMetric_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_172
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
         ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
            ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))
-- Function.Metric.Nat.Bundles.Metric._.antisym
d_antisym_390 ::
  T_Metric_364 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_390 :: T_Metric_364
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
d_antisym_390 = T_Metric_364
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.cong
d_cong_392 ::
  T_Metric_364 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_392 :: T_Metric_364
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_392 = T_Metric_364
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.isEquivalence
d_isEquivalence_394 ::
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_394 :: T_Metric_364 -> T_IsEquivalence_26
d_isEquivalence_394 T_Metric_364
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                        ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.isPartialOrder
d_isPartialOrder_396 ::
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_396 :: T_Metric_364 -> T_IsPartialOrder_162
d_isPartialOrder_396 T_Metric_364
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                  ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.isPreMetric
d_isPreMetric_398 ::
  T_Metric_364 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_96
d_isPreMetric_398 :: T_Metric_364 -> T_IsPreMetric_96
d_isPreMetric_398 T_Metric_364
v0
  = (T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96)
-> AgdaAny -> T_IsPreMetric_96
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
         ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
            ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))
-- Function.Metric.Nat.Bundles.Metric._.isPreorder
d_isPreorder_400 ::
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_400 :: T_Metric_364 -> T_IsPreorder_70
d_isPreorder_400 T_Metric_364
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.isProtoMetric
d_isProtoMetric_402 ::
  T_Metric_364 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_402 :: T_Metric_364 -> T_IsProtoMetric_30
d_isProtoMetric_402 T_Metric_364
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
         ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
            ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
               ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0)))))
-- Function.Metric.Nat.Bundles.Metric._.isQuasiSemiMetric
d_isQuasiSemiMetric_404 ::
  T_Metric_364 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_404 :: T_Metric_364 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_404 T_Metric_364
v0
  = (T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe
      T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
      ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
         ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0)))
-- Function.Metric.Nat.Bundles.Metric._.isSemiMetric
d_isSemiMetric_406 ::
  T_Metric_364 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_232
d_isSemiMetric_406 :: T_Metric_364 -> T_IsSemiMetric_232
d_isSemiMetric_406 T_Metric_364
v0
  = (T_IsGeneralMetric_308 -> T_IsSemiMetric_232)
-> AgdaAny -> T_IsSemiMetric_232
forall a b. a -> b
coe
      T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
      ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))
-- Function.Metric.Nat.Bundles.Metric._.nonNegative
d_nonNegative_408 ::
  T_Metric_364 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_nonNegative_408 :: T_Metric_364 -> AgdaAny -> AgdaAny -> T__'8804'__18
d_nonNegative_408 T_Metric_364
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                  ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.refl
d_refl_410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_refl_410 :: () -> () -> T_Metric_364 -> Integer -> T__'8804'__18
d_refl_410 ~()
v0 ~()
v1 T_Metric_364
v2 = T_Metric_364 -> Integer -> T__'8804'__18
du_refl_410 T_Metric_364
v2
du_refl_410 ::
  T_Metric_364 -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_refl_410 :: T_Metric_364 -> Integer -> T__'8804'__18
du_refl_410 T_Metric_364
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny -> Integer -> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.reflexive
d_reflexive_412 ::
  T_Metric_364 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_reflexive_412 :: T_Metric_364
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
d_reflexive_412 T_Metric_364
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                        ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.sym
d_sym_414 ::
  T_Metric_364 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_414 :: T_Metric_364 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_414 = T_Metric_364 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.trans
d_trans_416 ::
  T_Metric_364 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_trans_416 :: T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
d_trans_416 T_Metric_364
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                        ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.triangle
d_triangle_418 ::
  T_Metric_364 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_triangle_418 :: T_Metric_364 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
d_triangle_418 T_Metric_364
v0
  = (T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
forall a b. a -> b
coe
      T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_triangle_320
      ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))
-- Function.Metric.Nat.Bundles.Metric._.≈-isEquivalence
d_'8776''45'isEquivalence_420 ::
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_420 :: T_Metric_364 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_420 T_Metric_364
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                  ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.≈⇒0
d_'8776''8658'0_422 ::
  T_Metric_364 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_422 :: T_Metric_364 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_422 = T_Metric_364 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.∼-resp-≈
d_'8764''45'resp'45''8776'_424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_424 :: () -> () -> T_Metric_364 -> T_Σ_14
d_'8764''45'resp'45''8776'_424 ~()
v0 ~()
v1 T_Metric_364
v2
  = T_Metric_364 -> T_Σ_14
du_'8764''45'resp'45''8776'_424 T_Metric_364
v2
du_'8764''45'resp'45''8776'_424 ::
  T_Metric_364 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_424 :: T_Metric_364 -> T_Σ_14
du_'8764''45'resp'45''8776'_424 T_Metric_364
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'691''45''8776'_426 :: ()
-> ()
-> T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'691''45''8776'_426 ~()
v0 ~()
v1 T_Metric_364
v2
  = T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_426 T_Metric_364
v2
du_'8764''45'resp'691''45''8776'_426 ::
  T_Metric_364 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'691''45''8776'_426 :: T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_426 T_Metric_364
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'737''45''8776'_428 :: ()
-> ()
-> T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'737''45''8776'_428 ~()
v0 ~()
v1 T_Metric_364
v2
  = T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_428 T_Metric_364
v2
du_'8764''45'resp'737''45''8776'_428 ::
  T_Metric_364 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'737''45''8776'_428 :: T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_428 T_Metric_364
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.isPartialEquivalence
d_isPartialEquivalence_432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_432 :: () -> () -> T_Metric_364 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_432 ~()
v0 ~()
v1 T_Metric_364
v2
  = T_Metric_364 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_432 T_Metric_364
v2
du_isPartialEquivalence_432 ::
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_432 :: T_Metric_364 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_432 T_Metric_364
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsProtoMetric_30 -> T_IsEquivalence_26
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_434 :: T_Metric_364 -> AgdaAny -> AgdaAny
d_refl_434 :: T_Metric_364 -> AgdaAny -> AgdaAny
d_refl_434 T_Metric_364
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.reflexive
d_reflexive_436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_436 :: ()
-> ()
-> T_Metric_364
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_436 ~()
v0 ~()
v1 T_Metric_364
v2 = T_Metric_364 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_436 T_Metric_364
v2
du_reflexive_436 ::
  T_Metric_364 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_436 :: T_Metric_364 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_436 T_Metric_364
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsProtoMetric_30 -> T_IsEquivalence_26
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_438 ::
  T_Metric_364 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_438 :: T_Metric_364 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_438 T_Metric_364
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.trans
d_trans_440 ::
  T_Metric_364 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_440 :: T_Metric_364
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_440 T_Metric_364
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_Metric_364 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.Eq.isPartialEquivalence
d_isPartialEquivalence_444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_444 :: () -> () -> T_Metric_364 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_444 ~()
v0 ~()
v1 T_Metric_364
v2
  = T_Metric_364 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_Metric_364
v2
du_isPartialEquivalence_444 ::
  T_Metric_364 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_444 :: T_Metric_364 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_Metric_364
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
v7
                            = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                                (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                              (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v7)))))))))
-- Function.Metric.Nat.Bundles.Metric._.Eq.refl
d_refl_446 ::
  T_Metric_364 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_446 :: T_Metric_364 -> Integer -> T__'8801'__12
d_refl_446 = T_Metric_364 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.reflexive
d_reflexive_448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_448 :: ()
-> ()
-> T_Metric_364
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_448 = ()
-> ()
-> T_Metric_364
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.sym
d_sym_450 ::
  T_Metric_364 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_450 :: T_Metric_364
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_450 = T_Metric_364
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.trans
d_trans_452 ::
  T_Metric_364 ->
  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_452 :: T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_452 = T_Metric_364
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric.semiMetric
d_semiMetric_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 -> T_SemiMetric_266
d_semiMetric_454 :: () -> () -> T_Metric_364 -> T_SemiMetric_266
d_semiMetric_454 ~()
v0 ~()
v1 T_Metric_364
v2 = T_Metric_364 -> T_SemiMetric_266
du_semiMetric_454 T_Metric_364
v2
du_semiMetric_454 :: T_Metric_364 -> T_SemiMetric_266
du_semiMetric_454 :: T_Metric_364 -> T_SemiMetric_266
du_semiMetric_454 T_Metric_364
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsSemiMetric_232 -> T_SemiMetric_266)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_232
-> T_SemiMetric_266
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_232 -> T_SemiMetric_266
C_SemiMetric'46'constructor_4673 (T_Metric_364 -> AgdaAny -> AgdaAny -> Integer
d_d_382 (T_Metric_364 -> T_Metric_364
forall a b. a -> b
coe T_Metric_364
v0))
      (T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
         ((T_Metric_364 -> T_IsGeneralMetric_308)
-> AgdaAny -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_Metric_364 -> T_IsGeneralMetric_308
d_isMetric_384 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0)))
-- Function.Metric.Nat.Bundles.Metric._.preMetric
d_preMetric_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 -> T_PreMetric_90
d_preMetric_458 :: () -> () -> T_Metric_364 -> T_PreMetric_90
d_preMetric_458 ~()
v0 ~()
v1 T_Metric_364
v2 = T_Metric_364 -> T_PreMetric_90
du_preMetric_458 T_Metric_364
v2
du_preMetric_458 :: T_Metric_364 -> T_PreMetric_90
du_preMetric_458 :: T_Metric_364 -> T_PreMetric_90
du_preMetric_458 T_Metric_364
v0
  = let v1 :: t
v1 = (T_Metric_364 -> T_SemiMetric_266) -> AgdaAny -> t
forall a b. a -> b
coe T_Metric_364 -> T_SemiMetric_266
du_semiMetric_454 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny -> T_PreMetric_90
forall a b. a -> b
coe ((T_QuasiSemiMetric_174 -> T_PreMetric_90) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 ((T_SemiMetric_266 -> T_QuasiSemiMetric_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Metric.Nat.Bundles.Metric._.protoMetric
d_protoMetric_460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 -> T_ProtoMetric_12
d_protoMetric_460 :: () -> () -> T_Metric_364 -> T_ProtoMetric_12
d_protoMetric_460 ~()
v0 ~()
v1 T_Metric_364
v2 = T_Metric_364 -> T_ProtoMetric_12
du_protoMetric_460 T_Metric_364
v2
du_protoMetric_460 :: T_Metric_364 -> T_ProtoMetric_12
du_protoMetric_460 :: T_Metric_364 -> T_ProtoMetric_12
du_protoMetric_460 T_Metric_364
v0
  = let v1 :: t
v1 = (T_Metric_364 -> T_SemiMetric_266) -> AgdaAny -> t
forall a b. a -> b
coe T_Metric_364 -> T_SemiMetric_266
du_semiMetric_454 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiMetric_266 -> T_QuasiSemiMetric_174) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_PreMetric_90 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_ProtoMetric_12
du_protoMetric_168 ((T_QuasiSemiMetric_174 -> T_PreMetric_90) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Metric.Nat.Bundles.Metric._.quasiSemiMetric
d_quasiSemiMetric_462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_364 -> T_QuasiSemiMetric_174
d_quasiSemiMetric_462 :: () -> () -> T_Metric_364 -> T_QuasiSemiMetric_174
d_quasiSemiMetric_462 ~()
v0 ~()
v1 T_Metric_364
v2 = T_Metric_364 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_462 T_Metric_364
v2
du_quasiSemiMetric_462 :: T_Metric_364 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_462 :: T_Metric_364 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_462 T_Metric_364
v0
  = (T_SemiMetric_266 -> T_QuasiSemiMetric_174)
-> AgdaAny -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 ((T_Metric_364 -> T_SemiMetric_266) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_364 -> T_SemiMetric_266
du_semiMetric_454 (T_Metric_364 -> AgdaAny
forall a b. a -> b
coe T_Metric_364
v0))
-- Function.Metric.Nat.Bundles.UltraMetric
d_UltraMetric_468 :: p -> p -> ()
d_UltraMetric_468 p
a0 p
a1 = ()
data T_UltraMetric_468
  = C_UltraMetric'46'constructor_7973 (AgdaAny -> AgdaAny -> Integer)
                                      MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_308
-- Function.Metric.Nat.Bundles.UltraMetric.Carrier
d_Carrier_482 :: T_UltraMetric_468 -> ()
d_Carrier_482 :: T_UltraMetric_468 -> ()
d_Carrier_482 = T_UltraMetric_468 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._≈_
d__'8776'__484 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> ()
d__'8776'__484 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> ()
d__'8776'__484 = T_UltraMetric_468 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric.d
d_d_486 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> Integer
d_d_486 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> Integer
d_d_486 T_UltraMetric_468
v0
  = case T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0 of
      C_UltraMetric'46'constructor_7973 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_308
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_UltraMetric_468
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.UltraMetric.isUltraMetric
d_isUltraMetric_488 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_308
d_isUltraMetric_488 :: T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 T_UltraMetric_468
v0
  = case T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0 of
      C_UltraMetric'46'constructor_7973 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_308
v4 -> T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v4
      T_UltraMetric_468
_ -> T_IsGeneralMetric_308
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.UltraMetric._.0⇒≈
d_0'8658''8776'_492 ::
  T_UltraMetric_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_492 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_492 T_UltraMetric_468
v0
  = (T_IsQuasiSemiMetric_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_172
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
         ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
            ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))
-- Function.Metric.Nat.Bundles.UltraMetric._.antisym
d_antisym_494 ::
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_494 :: T_UltraMetric_468
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
d_antisym_494 = T_UltraMetric_468
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.cong
d_cong_496 ::
  T_UltraMetric_468 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_496 :: T_UltraMetric_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_496 = T_UltraMetric_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.isEquivalence
d_isEquivalence_498 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_498 :: T_UltraMetric_468 -> T_IsEquivalence_26
d_isEquivalence_498 T_UltraMetric_468
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                        ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPartialOrder
d_isPartialOrder_500 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_500 :: T_UltraMetric_468 -> T_IsPartialOrder_162
d_isPartialOrder_500 T_UltraMetric_468
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                  ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPreMetric
d_isPreMetric_502 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_96
d_isPreMetric_502 :: T_UltraMetric_468 -> T_IsPreMetric_96
d_isPreMetric_502 T_UltraMetric_468
v0
  = (T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96)
-> AgdaAny -> T_IsPreMetric_96
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
      ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
         ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
            ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPreorder
d_isPreorder_504 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_504 :: T_UltraMetric_468 -> T_IsPreorder_70
d_isPreorder_504 T_UltraMetric_468
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isProtoMetric
d_isProtoMetric_506 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_506 :: T_UltraMetric_468 -> T_IsProtoMetric_30
d_isProtoMetric_506 T_UltraMetric_468
v0
  = (T_IsPreMetric_96 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
      ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
         ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
            ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
               ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0)))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_508 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_508 :: T_UltraMetric_468 -> T_IsQuasiSemiMetric_162
d_isQuasiSemiMetric_508 T_UltraMetric_468
v0
  = (T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe
      T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
      ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
         ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0)))
-- Function.Metric.Nat.Bundles.UltraMetric._.isSemiMetric
d_isSemiMetric_510 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_232
d_isSemiMetric_510 :: T_UltraMetric_468 -> T_IsSemiMetric_232
d_isSemiMetric_510 T_UltraMetric_468
v0
  = (T_IsGeneralMetric_308 -> T_IsSemiMetric_232)
-> AgdaAny -> T_IsSemiMetric_232
forall a b. a -> b
coe
      T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
      ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))
-- Function.Metric.Nat.Bundles.UltraMetric._.nonNegative
d_nonNegative_512 ::
  T_UltraMetric_468 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_nonNegative_512 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> T__'8804'__18
d_nonNegative_512 T_UltraMetric_468
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                  ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.refl
d_refl_514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_refl_514 :: () -> () -> T_UltraMetric_468 -> Integer -> T__'8804'__18
d_refl_514 ~()
v0 ~()
v1 T_UltraMetric_468
v2 = T_UltraMetric_468 -> Integer -> T__'8804'__18
du_refl_514 T_UltraMetric_468
v2
du_refl_514 ::
  T_UltraMetric_468 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_refl_514 :: T_UltraMetric_468 -> Integer -> T__'8804'__18
du_refl_514 T_UltraMetric_468
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny -> Integer -> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.reflexive
d_reflexive_516 ::
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_reflexive_516 :: T_UltraMetric_468
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
d_reflexive_516 T_UltraMetric_468
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                        ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.sym
d_sym_518 ::
  T_UltraMetric_468 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_518 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_518 = T_UltraMetric_468 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.trans
d_trans_520 ::
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_trans_520 :: T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
d_trans_520 T_UltraMetric_468
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__18
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_162
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
               ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                  ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                     ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                        ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.triangle
d_triangle_522 ::
  T_UltraMetric_468 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_triangle_522 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
d_triangle_522 T_UltraMetric_468
v0
  = (T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__18
forall a b. a -> b
coe
      T_IsGeneralMetric_308 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_triangle_320
      ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))
-- Function.Metric.Nat.Bundles.UltraMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_524 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_524 :: T_UltraMetric_468 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_524 T_UltraMetric_468
v0
  = (T_IsProtoMetric_30 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
      ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
         ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
            ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
               ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                  ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≈⇒0
d_'8776''8658'0_526 ::
  T_UltraMetric_468 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_526 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_526 = T_UltraMetric_468 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_528 :: () -> () -> T_UltraMetric_468 -> T_Σ_14
d_'8764''45'resp'45''8776'_528 ~()
v0 ~()
v1 T_UltraMetric_468
v2
  = T_UltraMetric_468 -> T_Σ_14
du_'8764''45'resp'45''8776'_528 T_UltraMetric_468
v2
du_'8764''45'resp'45''8776'_528 ::
  T_UltraMetric_468 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_528 :: T_UltraMetric_468 -> T_Σ_14
du_'8764''45'resp'45''8776'_528 T_UltraMetric_468
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'691''45''8776'_530 :: ()
-> ()
-> T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'691''45''8776'_530 ~()
v0 ~()
v1 T_UltraMetric_468
v2
  = T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_530 T_UltraMetric_468
v2
du_'8764''45'resp'691''45''8776'_530 ::
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'691''45''8776'_530 :: T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'691''45''8776'_530 T_UltraMetric_468
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8764''45'resp'737''45''8776'_532 :: ()
-> ()
-> T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
d_'8764''45'resp'737''45''8776'_532 ~()
v0 ~()
v1 T_UltraMetric_468
v2
  = T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_532 T_UltraMetric_468
v2
du_'8764''45'resp'737''45''8776'_532 ::
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'8764''45'resp'737''45''8776'_532 :: T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
du_'8764''45'resp'737''45''8776'_532 T_UltraMetric_468
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__18
-> T__'8804'__18
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                        ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                           (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_536 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_536 :: () -> () -> T_UltraMetric_468 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_536 ~()
v0 ~()
v1 T_UltraMetric_468
v2
  = T_UltraMetric_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_536 T_UltraMetric_468
v2
du_isPartialEquivalence_536 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_536 :: T_UltraMetric_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_536 T_UltraMetric_468
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsProtoMetric_30 -> T_IsEquivalence_26
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_538 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny
d_refl_538 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny
d_refl_538 T_UltraMetric_468
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.reflexive
d_reflexive_540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_540 :: ()
-> ()
-> T_UltraMetric_468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_540 ~()
v0 ~()
v1 T_UltraMetric_468
v2 = T_UltraMetric_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_540 T_UltraMetric_468
v2
du_reflexive_540 ::
  T_UltraMetric_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_540 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_540 T_UltraMetric_468
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsProtoMetric_30 -> T_IsEquivalence_26
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_542 ::
  T_UltraMetric_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_542 :: T_UltraMetric_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_542 T_UltraMetric_468
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.trans
d_trans_544 ::
  T_UltraMetric_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_544 :: T_UltraMetric_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_544 T_UltraMetric_468
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_96 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
            ((T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
               ((T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                  ((T_IsGeneralMetric_308 -> T_IsSemiMetric_232) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                     ((T_UltraMetric_468 -> T_IsGeneralMetric_308) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_548 :: () -> () -> T_UltraMetric_468 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_548 ~()
v0 ~()
v1 T_UltraMetric_468
v2
  = T_UltraMetric_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_548 T_UltraMetric_468
v2
du_isPartialEquivalence_548 ::
  T_UltraMetric_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_548 :: T_UltraMetric_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_548 T_UltraMetric_468
v0
  = let v1 :: T_IsGeneralMetric_308
v1 = T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_232
v2
             = T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
                 (T_IsGeneralMetric_308 -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_IsGeneralMetric_308
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_162
v3
                = T_IsSemiMetric_232 -> T_IsQuasiSemiMetric_162
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_240
                    (T_IsSemiMetric_232 -> T_IsSemiMetric_232
forall a b. a -> b
coe T_IsSemiMetric_232
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_96
v4
                   = T_IsQuasiSemiMetric_162 -> T_IsPreMetric_96
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_170
                       (T_IsQuasiSemiMetric_162 -> T_IsQuasiSemiMetric_162
forall a b. a -> b
coe T_IsQuasiSemiMetric_162
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_96 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_104
                          (T_IsPreMetric_96 -> T_IsPreMetric_96
forall a b. a -> b
coe T_IsPreMetric_96
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_162
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_162
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_70
v7
                            = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                                (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                              (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v7)))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.refl
d_refl_550 ::
  T_UltraMetric_468 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_550 :: T_UltraMetric_468 -> Integer -> T__'8801'__12
d_refl_550 = T_UltraMetric_468 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.reflexive
d_reflexive_552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_552 :: ()
-> ()
-> T_UltraMetric_468
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_552 = ()
-> ()
-> T_UltraMetric_468
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.sym
d_sym_554 ::
  T_UltraMetric_468 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_554 :: T_UltraMetric_468
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_554 = T_UltraMetric_468
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.trans
d_trans_556 ::
  T_UltraMetric_468 ->
  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_556 :: T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_556 = T_UltraMetric_468
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric.semiMetric
d_semiMetric_558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 -> T_SemiMetric_266
d_semiMetric_558 :: () -> () -> T_UltraMetric_468 -> T_SemiMetric_266
d_semiMetric_558 ~()
v0 ~()
v1 T_UltraMetric_468
v2 = T_UltraMetric_468 -> T_SemiMetric_266
du_semiMetric_558 T_UltraMetric_468
v2
du_semiMetric_558 :: T_UltraMetric_468 -> T_SemiMetric_266
du_semiMetric_558 :: T_UltraMetric_468 -> T_SemiMetric_266
du_semiMetric_558 T_UltraMetric_468
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsSemiMetric_232 -> T_SemiMetric_266)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_232
-> T_SemiMetric_266
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_232 -> T_SemiMetric_266
C_SemiMetric'46'constructor_4673 (T_UltraMetric_468 -> AgdaAny -> AgdaAny -> Integer
d_d_486 (T_UltraMetric_468 -> T_UltraMetric_468
forall a b. a -> b
coe T_UltraMetric_468
v0))
      (T_IsGeneralMetric_308 -> T_IsSemiMetric_232
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_318
         ((T_UltraMetric_468 -> T_IsGeneralMetric_308)
-> AgdaAny -> T_IsGeneralMetric_308
forall a b. a -> b
coe T_UltraMetric_468 -> T_IsGeneralMetric_308
d_isUltraMetric_488 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0)))
-- Function.Metric.Nat.Bundles.UltraMetric._.preMetric
d_preMetric_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 -> T_PreMetric_90
d_preMetric_562 :: () -> () -> T_UltraMetric_468 -> T_PreMetric_90
d_preMetric_562 ~()
v0 ~()
v1 T_UltraMetric_468
v2 = T_UltraMetric_468 -> T_PreMetric_90
du_preMetric_562 T_UltraMetric_468
v2
du_preMetric_562 :: T_UltraMetric_468 -> T_PreMetric_90
du_preMetric_562 :: T_UltraMetric_468 -> T_PreMetric_90
du_preMetric_562 T_UltraMetric_468
v0
  = let v1 :: t
v1 = (T_UltraMetric_468 -> T_SemiMetric_266) -> AgdaAny -> t
forall a b. a -> b
coe T_UltraMetric_468 -> T_SemiMetric_266
du_semiMetric_558 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny -> T_PreMetric_90
forall a b. a -> b
coe ((T_QuasiSemiMetric_174 -> T_PreMetric_90) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 ((T_SemiMetric_266 -> T_QuasiSemiMetric_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Metric.Nat.Bundles.UltraMetric._.protoMetric
d_protoMetric_564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 -> T_ProtoMetric_12
d_protoMetric_564 :: () -> () -> T_UltraMetric_468 -> T_ProtoMetric_12
d_protoMetric_564 ~()
v0 ~()
v1 T_UltraMetric_468
v2 = T_UltraMetric_468 -> T_ProtoMetric_12
du_protoMetric_564 T_UltraMetric_468
v2
du_protoMetric_564 :: T_UltraMetric_468 -> T_ProtoMetric_12
du_protoMetric_564 :: T_UltraMetric_468 -> T_ProtoMetric_12
du_protoMetric_564 T_UltraMetric_468
v0
  = let v1 :: t
v1 = (T_UltraMetric_468 -> T_SemiMetric_266) -> AgdaAny -> t
forall a b. a -> b
coe T_UltraMetric_468 -> T_SemiMetric_266
du_semiMetric_558 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiMetric_266 -> T_QuasiSemiMetric_174) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_PreMetric_90 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_90 -> T_ProtoMetric_12
du_protoMetric_168 ((T_QuasiSemiMetric_174 -> T_PreMetric_90) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_174 -> T_PreMetric_90
du_preMetric_256 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Metric.Nat.Bundles.UltraMetric._.quasiSemiMetric
d_quasiSemiMetric_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_468 -> T_QuasiSemiMetric_174
d_quasiSemiMetric_566 :: () -> () -> T_UltraMetric_468 -> T_QuasiSemiMetric_174
d_quasiSemiMetric_566 ~()
v0 ~()
v1 T_UltraMetric_468
v2 = T_UltraMetric_468 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_566 T_UltraMetric_468
v2
du_quasiSemiMetric_566 ::
  T_UltraMetric_468 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_566 :: T_UltraMetric_468 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_566 T_UltraMetric_468
v0
  = (T_SemiMetric_266 -> T_QuasiSemiMetric_174)
-> AgdaAny -> T_QuasiSemiMetric_174
forall a b. a -> b
coe T_SemiMetric_266 -> T_QuasiSemiMetric_174
du_quasiSemiMetric_352 ((T_UltraMetric_468 -> T_SemiMetric_266) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468 -> T_SemiMetric_266
du_semiMetric_558 (T_UltraMetric_468 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_468
v0))