{-# 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'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_36 :: T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_36 = T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.cong
d_cong_38 ::
  T_ProtoMetric_12 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_38 :: T_ProtoMetric_12
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_38 = T_ProtoMetric_12
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.isEquivalence
d_isEquivalence_40 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174
d_isPartialOrder_42 :: T_ProtoMetric_12 -> T_IsPartialOrder_174
d_isPartialOrder_42 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0)))
-- Function.Metric.Nat.Bundles.ProtoMetric._.nonNegative
d_nonNegative_46 ::
  T_ProtoMetric_12 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_46 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_46 T_ProtoMetric_12
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))
-- Function.Metric.Nat.Bundles.ProtoMetric._.refl
d_refl_48 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_48 :: () -> () -> T_ProtoMetric_12 -> Integer -> T__'8804'__22
d_refl_48 ~()
v0 ~()
v1 T_ProtoMetric_12
v2 = T_ProtoMetric_12 -> Integer -> T__'8804'__22
du_refl_48 T_ProtoMetric_12
v2
du_refl_48 ::
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_48 :: T_ProtoMetric_12 -> Integer -> T__'8804'__22
du_refl_48 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.reflexive
d_reflexive_50 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_50 :: T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_50 T_ProtoMetric_12
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_ProtoMetric_12 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> AgdaAny
forall a b. a -> b
coe T_ProtoMetric_12
v0))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.trans
d_trans_52 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_52 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_52 T_ProtoMetric_12
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_58 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_58 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_58 T_ProtoMetric_12
v2
du_'8764''45'resp'691''45''8776'_58 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_58 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_58 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_60 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_60 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_60 T_ProtoMetric_12
v2
du_'8764''45'resp'737''45''8776'_60 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_60 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_60 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_62 :: () -> () -> T_ProtoMetric_12 -> T_Σ_14
d_'8818''45'resp'45''8776'_62 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_Σ_14
du_'8818''45'resp'45''8776'_62 T_ProtoMetric_12
v2
du_'8818''45'resp'45''8776'_62 ::
  T_ProtoMetric_12 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_62 :: T_ProtoMetric_12 -> T_Σ_14
du_'8818''45'resp'45''8776'_62 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_64 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_64 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_64 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_64 T_ProtoMetric_12
v2
du_'8818''45'resp'691''45''8776'_64 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_64 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_64 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_66 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_66 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_66 T_ProtoMetric_12
v2
du_'8818''45'resp'737''45''8776'_66 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_66 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_66 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_70 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_70 :: () -> () -> T_ProtoMetric_12 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_70 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_70 T_ProtoMetric_12
v2
du_isPartialEquivalence_70 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_70 :: T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_70 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_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_72 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny
d_refl_72 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny
d_refl_72 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_74 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_74 :: ()
-> ()
-> T_ProtoMetric_12
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_74 ~()
v0 ~()
v1 T_ProtoMetric_12
v2 = T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_74 T_ProtoMetric_12
v2
du_reflexive_74 ::
  T_ProtoMetric_12 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_74 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_74 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_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_76 ::
  T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_76 :: T_ProtoMetric_12 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_76 T_ProtoMetric_12
v0
  = (T_IsEquivalence_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_78 ::
  T_ProtoMetric_12 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_78 :: T_ProtoMetric_12
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_78 T_ProtoMetric_12
v0
  = (T_IsEquivalence_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_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_82 :: () -> () -> T_ProtoMetric_12 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_82 ~()
v0 ~()
v1 T_ProtoMetric_12
v2
  = T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_82 T_ProtoMetric_12
v2
du_isPartialEquivalence_82 ::
  T_ProtoMetric_12 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_82 :: T_ProtoMetric_12 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_82 T_ProtoMetric_12
v0
  = let v1 :: T_IsProtoMetric_30
v1 = T_ProtoMetric_12 -> T_IsProtoMetric_30
d_isProtoMetric_32 (T_ProtoMetric_12 -> T_ProtoMetric_12
forall a b. a -> b
coe T_ProtoMetric_12
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2
             = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.refl
d_refl_84 ::
  T_ProtoMetric_12 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_84 :: T_ProtoMetric_12 -> Integer -> T__'8801'__12
d_refl_84 = T_ProtoMetric_12 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.reflexive
d_reflexive_86 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_86 :: ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_86 = ()
-> ()
-> T_ProtoMetric_12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.sym
d_sym_88 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_88 :: T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_88 = T_ProtoMetric_12
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.ProtoMetric._.Eq.trans
d_trans_90 ::
  T_ProtoMetric_12 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_90 :: T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_90 = T_ProtoMetric_12
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric
d_PreMetric_96 :: p -> p -> ()
d_PreMetric_96 p
a0 p
a1 = ()
data T_PreMetric_96
  = C_PreMetric'46'constructor_1629 (AgdaAny -> AgdaAny -> Integer)
                                    MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_102
-- Function.Metric.Nat.Bundles.PreMetric.Carrier
d_Carrier_110 :: T_PreMetric_96 -> ()
d_Carrier_110 :: T_PreMetric_96 -> ()
d_Carrier_110 = T_PreMetric_96 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._≈_
d__'8776'__112 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> ()
d__'8776'__112 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> ()
d__'8776'__112 = T_PreMetric_96 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric.d
d_d_114 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> Integer
d_d_114 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> Integer
d_d_114 T_PreMetric_96
v0
  = case T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0 of
      C_PreMetric'46'constructor_1629 AgdaAny -> AgdaAny -> Integer
v3 T_IsPreMetric_102
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_PreMetric_96
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.PreMetric.isPreMetric
d_isPreMetric_116 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_102
d_isPreMetric_116 :: T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 T_PreMetric_96
v0
  = case T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0 of
      C_PreMetric'46'constructor_1629 AgdaAny -> AgdaAny -> Integer
v3 T_IsPreMetric_102
v4 -> T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4
      T_PreMetric_96
_ -> T_IsPreMetric_102
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.PreMetric._.antisym
d_antisym_120 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_120 :: T_PreMetric_96
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_120 = T_PreMetric_96
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.cong
d_cong_122 ::
  T_PreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_122 :: T_PreMetric_96
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_122 = T_PreMetric_96
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.isEquivalence
d_isEquivalence_124 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_124 :: T_PreMetric_96 -> T_IsEquivalence_26
d_isEquivalence_124 T_PreMetric_96
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.isPartialOrder
d_isPartialOrder_126 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_126 :: T_PreMetric_96 -> T_IsPartialOrder_174
d_isPartialOrder_126 T_PreMetric_96
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.isPreorder
d_isPreorder_128 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_128 :: T_PreMetric_96 -> T_IsPreorder_70
d_isPreorder_128 T_PreMetric_96
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.isProtoMetric
d_isProtoMetric_130 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_130 :: T_PreMetric_96 -> T_IsProtoMetric_30
d_isProtoMetric_130 T_PreMetric_96
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
      ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0))
-- Function.Metric.Nat.Bundles.PreMetric._.nonNegative
d_nonNegative_132 ::
  T_PreMetric_96 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_132 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_132 T_PreMetric_96
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.refl
d_refl_134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_134 :: () -> () -> T_PreMetric_96 -> Integer -> T__'8804'__22
d_refl_134 ~()
v0 ~()
v1 T_PreMetric_96
v2 = T_PreMetric_96 -> Integer -> T__'8804'__22
du_refl_134 T_PreMetric_96
v2
du_refl_134 ::
  T_PreMetric_96 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_134 :: T_PreMetric_96 -> Integer -> T__'8804'__22
du_refl_134 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.reflexive
d_reflexive_136 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_136 :: T_PreMetric_96
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_136 T_PreMetric_96
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.trans
d_trans_138 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_138 :: T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_138 T_PreMetric_96
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0)))))
-- Function.Metric.Nat.Bundles.PreMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_140 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_140 :: T_PreMetric_96 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_140 T_PreMetric_96
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0)))
-- Function.Metric.Nat.Bundles.PreMetric._.≈⇒0
d_'8776''8658'0_142 ::
  T_PreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_142 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_142 = T_PreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_144 :: () -> () -> T_PreMetric_96 -> T_Σ_14
d_'8764''45'resp'45''8776'_144 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96 -> T_Σ_14
du_'8764''45'resp'45''8776'_144 T_PreMetric_96
v2
du_'8764''45'resp'45''8776'_144 ::
  T_PreMetric_96 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_144 :: T_PreMetric_96 -> T_Σ_14
du_'8764''45'resp'45''8776'_144 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_146 :: ()
-> ()
-> T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_146 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_146 T_PreMetric_96
v2
du_'8764''45'resp'691''45''8776'_146 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_146 :: T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_146 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_148 :: ()
-> ()
-> T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_148 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_148 T_PreMetric_96
v2
du_'8764''45'resp'737''45''8776'_148 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_148 :: T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_148 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_150 :: () -> () -> T_PreMetric_96 -> T_Σ_14
d_'8818''45'resp'45''8776'_150 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96 -> T_Σ_14
du_'8818''45'resp'45''8776'_150 T_PreMetric_96
v2
du_'8818''45'resp'45''8776'_150 ::
  T_PreMetric_96 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_150 :: T_PreMetric_96 -> T_Σ_14
du_'8818''45'resp'45''8776'_150 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_152 :: ()
-> ()
-> T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_152 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_152 T_PreMetric_96
v2
du_'8818''45'resp'691''45''8776'_152 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_152 :: T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_152 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_154 :: ()
-> ()
-> T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_154 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_154 T_PreMetric_96
v2
du_'8818''45'resp'737''45''8776'_154 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_154 :: T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_154 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_158 :: () -> () -> T_PreMetric_96 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_158 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_158 T_PreMetric_96
v2
du_isPartialEquivalence_158 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_158 :: T_PreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_158 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsProtoMetric_30 -> T_IsEquivalence_26
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_160 :: T_PreMetric_96 -> AgdaAny -> AgdaAny
d_refl_160 :: T_PreMetric_96 -> AgdaAny -> AgdaAny
d_refl_160 T_PreMetric_96
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.reflexive
d_reflexive_162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_162 :: ()
-> ()
-> T_PreMetric_96
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_162 ~()
v0 ~()
v1 T_PreMetric_96
v2 = T_PreMetric_96 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_162 T_PreMetric_96
v2
du_reflexive_162 ::
  T_PreMetric_96 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_162 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_162 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsProtoMetric_30 -> T_IsEquivalence_26
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_164 ::
  T_PreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_164 :: T_PreMetric_96 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_164 T_PreMetric_96
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.EqC.trans
d_trans_166 ::
  T_PreMetric_96 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_166 :: T_PreMetric_96
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_166 T_PreMetric_96
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsEquivalence_26
MAlonzo.Code.Function.Metric.Structures.d_'8776''45'isEquivalence_44
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_PreMetric_96 -> T_IsPreMetric_102) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0))))
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_170 :: () -> () -> T_PreMetric_96 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_170 ~()
v0 ~()
v1 T_PreMetric_96
v2
  = T_PreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_170 T_PreMetric_96
v2
du_isPartialEquivalence_170 ::
  T_PreMetric_96 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_170 :: T_PreMetric_96 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_170 T_PreMetric_96
v0
  = let v1 :: T_IsPreMetric_102
v1 = T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsProtoMetric_30
v2
             = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                 (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3
                = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                       (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.refl
d_refl_172 ::
  T_PreMetric_96 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_172 :: T_PreMetric_96 -> Integer -> T__'8801'__12
d_refl_172 = T_PreMetric_96 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.reflexive
d_reflexive_174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_174 :: ()
-> ()
-> T_PreMetric_96
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_174 = ()
-> ()
-> T_PreMetric_96
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.sym
d_sym_176 ::
  T_PreMetric_96 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_176 :: T_PreMetric_96
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_176 = T_PreMetric_96
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric._.Eq.trans
d_trans_178 ::
  T_PreMetric_96 ->
  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_178 :: T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_178 = T_PreMetric_96
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.PreMetric.protoMetric
d_protoMetric_180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_PreMetric_96 -> T_ProtoMetric_12
d_protoMetric_180 :: () -> () -> T_PreMetric_96 -> T_ProtoMetric_12
d_protoMetric_180 ~()
v0 ~()
v1 T_PreMetric_96
v2 = T_PreMetric_96 -> T_ProtoMetric_12
du_protoMetric_180 T_PreMetric_96
v2
du_protoMetric_180 :: T_PreMetric_96 -> T_ProtoMetric_12
du_protoMetric_180 :: T_PreMetric_96 -> T_ProtoMetric_12
du_protoMetric_180 T_PreMetric_96
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_96 -> AgdaAny -> AgdaAny -> Integer
d_d_114 (T_PreMetric_96 -> T_PreMetric_96
forall a b. a -> b
coe T_PreMetric_96
v0))
      (T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_PreMetric_96 -> T_IsPreMetric_102)
-> AgdaAny -> T_IsPreMetric_102
forall a b. a -> b
coe T_PreMetric_96 -> T_IsPreMetric_102
d_isPreMetric_116 (T_PreMetric_96 -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric
d_QuasiSemiMetric_186 :: p -> p -> ()
d_QuasiSemiMetric_186 p
a0 p
a1 = ()
data T_QuasiSemiMetric_186
  = C_QuasiSemiMetric'46'constructor_3255 (AgdaAny ->
                                           AgdaAny -> Integer)
                                          MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_174
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.Carrier
d_Carrier_200 :: T_QuasiSemiMetric_186 -> ()
d_Carrier_200 :: T_QuasiSemiMetric_186 -> ()
d_Carrier_200 = T_QuasiSemiMetric_186 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._≈_
d__'8776'__202 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> ()
d__'8776'__202 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> ()
d__'8776'__202 = T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.d
d_d_204 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> Integer
d_d_204 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> Integer
d_d_204 T_QuasiSemiMetric_186
v0
  = case T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0 of
      C_QuasiSemiMetric'46'constructor_3255 AgdaAny -> AgdaAny -> Integer
v3 T_IsQuasiSemiMetric_174
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_QuasiSemiMetric_186
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.isQuasiSemiMetric
d_isQuasiSemiMetric_206 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 :: T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 T_QuasiSemiMetric_186
v0
  = case T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0 of
      C_QuasiSemiMetric'46'constructor_3255 AgdaAny -> AgdaAny -> Integer
v3 T_IsQuasiSemiMetric_174
v4 -> T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v4
      T_QuasiSemiMetric_186
_ -> T_IsQuasiSemiMetric_174
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.0⇒≈
d_0'8658''8776'_210 ::
  T_QuasiSemiMetric_186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_210 :: T_QuasiSemiMetric_186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_210 T_QuasiSemiMetric_186
v0
  = (T_IsQuasiSemiMetric_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_184
      ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.antisym
d_antisym_212 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_212 :: T_QuasiSemiMetric_186
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_212 = T_QuasiSemiMetric_186
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.cong
d_cong_214 ::
  T_QuasiSemiMetric_186 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_214 :: T_QuasiSemiMetric_186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_214 = T_QuasiSemiMetric_186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isEquivalence
d_isEquivalence_216 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_216 :: T_QuasiSemiMetric_186 -> T_IsEquivalence_26
d_isEquivalence_216 T_QuasiSemiMetric_186
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPartialOrder
d_isPartialOrder_218 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_218 :: T_QuasiSemiMetric_186 -> T_IsPartialOrder_174
d_isPartialOrder_218 T_QuasiSemiMetric_186
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPreMetric
d_isPreMetric_220 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_102
d_isPreMetric_220 :: T_QuasiSemiMetric_186 -> T_IsPreMetric_102
d_isPreMetric_220 T_QuasiSemiMetric_186
v0
  = (T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> T_IsPreMetric_102
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
      ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isPreorder
d_isPreorder_222 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_222 :: T_QuasiSemiMetric_186 -> T_IsPreorder_70
d_isPreorder_222 T_QuasiSemiMetric_186
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.isProtoMetric
d_isProtoMetric_224 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_224 :: T_QuasiSemiMetric_186 -> T_IsProtoMetric_30
d_isProtoMetric_224 T_QuasiSemiMetric_186
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
         ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.nonNegative
d_nonNegative_226 ::
  T_QuasiSemiMetric_186 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_226 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_226 T_QuasiSemiMetric_186
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.refl
d_refl_228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_228 :: () -> () -> T_QuasiSemiMetric_186 -> Integer -> T__'8804'__22
d_refl_228 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2 = T_QuasiSemiMetric_186 -> Integer -> T__'8804'__22
du_refl_228 T_QuasiSemiMetric_186
v2
du_refl_228 ::
  T_QuasiSemiMetric_186 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_228 :: T_QuasiSemiMetric_186 -> Integer -> T__'8804'__22
du_refl_228 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.reflexive
d_reflexive_230 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_230 :: T_QuasiSemiMetric_186
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_230 T_QuasiSemiMetric_186
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.trans
d_trans_232 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_232 :: T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_232 T_QuasiSemiMetric_186
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_234 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_234 :: T_QuasiSemiMetric_186 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_234 T_QuasiSemiMetric_186
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≈⇒0
d_'8776''8658'0_236 ::
  T_QuasiSemiMetric_186 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_236 :: T_QuasiSemiMetric_186
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_236 = T_QuasiSemiMetric_186
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_238 :: () -> () -> T_QuasiSemiMetric_186 -> T_Σ_14
d_'8764''45'resp'45''8776'_238 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186 -> T_Σ_14
du_'8764''45'resp'45''8776'_238 T_QuasiSemiMetric_186
v2
du_'8764''45'resp'45''8776'_238 ::
  T_QuasiSemiMetric_186 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_238 :: T_QuasiSemiMetric_186 -> T_Σ_14
du_'8764''45'resp'45''8776'_238 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_240 :: ()
-> ()
-> T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_240 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_240 T_QuasiSemiMetric_186
v2
du_'8764''45'resp'691''45''8776'_240 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_240 :: T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_240 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_242 :: ()
-> ()
-> T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_242 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_242 T_QuasiSemiMetric_186
v2
du_'8764''45'resp'737''45''8776'_242 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_242 :: T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_242 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_244 :: () -> () -> T_QuasiSemiMetric_186 -> T_Σ_14
d_'8818''45'resp'45''8776'_244 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186 -> T_Σ_14
du_'8818''45'resp'45''8776'_244 T_QuasiSemiMetric_186
v2
du_'8818''45'resp'45''8776'_244 ::
  T_QuasiSemiMetric_186 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_244 :: T_QuasiSemiMetric_186 -> T_Σ_14
du_'8818''45'resp'45''8776'_244 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_246 :: ()
-> ()
-> T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_246 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_246 T_QuasiSemiMetric_186
v2
du_'8818''45'resp'691''45''8776'_246 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_246 :: T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_246 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_248 :: ()
-> ()
-> T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_248 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_248 T_QuasiSemiMetric_186
v2
du_'8818''45'resp'737''45''8776'_248 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_248 :: T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_248 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_252 :: () -> () -> T_QuasiSemiMetric_186 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_252 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_252 T_QuasiSemiMetric_186
v2
du_isPartialEquivalence_252 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_252 :: T_QuasiSemiMetric_186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_252 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsProtoMetric_30 -> T_IsEquivalence_26
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_254 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny
d_refl_254 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny
d_refl_254 T_QuasiSemiMetric_186
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.reflexive
d_reflexive_256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_256 :: ()
-> ()
-> T_QuasiSemiMetric_186
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_256 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2 = T_QuasiSemiMetric_186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_256 T_QuasiSemiMetric_186
v2
du_reflexive_256 ::
  T_QuasiSemiMetric_186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_256 :: T_QuasiSemiMetric_186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_256 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsProtoMetric_30 -> T_IsEquivalence_26
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_258 ::
  T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_258 :: T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_258 T_QuasiSemiMetric_186
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.EqC.trans
d_trans_260 ::
  T_QuasiSemiMetric_186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_260 :: T_QuasiSemiMetric_186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_260 T_QuasiSemiMetric_186
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0)))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_264 :: () -> () -> T_QuasiSemiMetric_186 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_264 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2
  = T_QuasiSemiMetric_186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_QuasiSemiMetric_186
v2
du_isPartialEquivalence_264 ::
  T_QuasiSemiMetric_186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_264 :: T_QuasiSemiMetric_186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_QuasiSemiMetric_186
v0
  = let v1 :: T_IsQuasiSemiMetric_174
v1 = T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreMetric_102
v2
             = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                 (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsProtoMetric_30
v3
                = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                    (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4
                   = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                          (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5)))))))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.refl
d_refl_266 ::
  T_QuasiSemiMetric_186 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_266 :: T_QuasiSemiMetric_186 -> Integer -> T__'8801'__12
d_refl_266 = T_QuasiSemiMetric_186 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.reflexive
d_reflexive_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_268 :: ()
-> ()
-> T_QuasiSemiMetric_186
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_268 = ()
-> ()
-> T_QuasiSemiMetric_186
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.sym
d_sym_270 ::
  T_QuasiSemiMetric_186 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_270 :: T_QuasiSemiMetric_186
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_270 = T_QuasiSemiMetric_186
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.Eq.trans
d_trans_272 ::
  T_QuasiSemiMetric_186 ->
  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_272 :: T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_272 = T_QuasiSemiMetric_186
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.QuasiSemiMetric.preMetric
d_preMetric_274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 -> T_PreMetric_96
d_preMetric_274 :: () -> () -> T_QuasiSemiMetric_186 -> T_PreMetric_96
d_preMetric_274 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2 = T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 T_QuasiSemiMetric_186
v2
du_preMetric_274 :: T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 :: T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 T_QuasiSemiMetric_186
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsPreMetric_102 -> T_PreMetric_96)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsPreMetric_102
-> T_PreMetric_96
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsPreMetric_102 -> T_PreMetric_96
C_PreMetric'46'constructor_1629 (T_QuasiSemiMetric_186 -> AgdaAny -> AgdaAny -> Integer
d_d_204 (T_QuasiSemiMetric_186 -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))
      (T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
         ((T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_206 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0)))
-- Function.Metric.Nat.Bundles.QuasiSemiMetric._.protoMetric
d_protoMetric_278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_QuasiSemiMetric_186 -> T_ProtoMetric_12
d_protoMetric_278 :: () -> () -> T_QuasiSemiMetric_186 -> T_ProtoMetric_12
d_protoMetric_278 ~()
v0 ~()
v1 T_QuasiSemiMetric_186
v2 = T_QuasiSemiMetric_186 -> T_ProtoMetric_12
du_protoMetric_278 T_QuasiSemiMetric_186
v2
du_protoMetric_278 :: T_QuasiSemiMetric_186 -> T_ProtoMetric_12
du_protoMetric_278 :: T_QuasiSemiMetric_186 -> T_ProtoMetric_12
du_protoMetric_278 T_QuasiSemiMetric_186
v0
  = (T_PreMetric_96 -> T_ProtoMetric_12) -> AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe T_PreMetric_96 -> T_ProtoMetric_12
du_protoMetric_180 ((T_QuasiSemiMetric_186 -> T_PreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 (T_QuasiSemiMetric_186 -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186
v0))
-- Function.Metric.Nat.Bundles.SemiMetric
d_SemiMetric_284 :: p -> p -> ()
d_SemiMetric_284 p
a0 p
a1 = ()
data T_SemiMetric_284
  = C_SemiMetric'46'constructor_4991 (AgdaAny -> AgdaAny -> Integer)
                                     MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_250
-- Function.Metric.Nat.Bundles.SemiMetric.Carrier
d_Carrier_298 :: T_SemiMetric_284 -> ()
d_Carrier_298 :: T_SemiMetric_284 -> ()
d_Carrier_298 = T_SemiMetric_284 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._≈_
d__'8776'__300 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> ()
d__'8776'__300 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> ()
d__'8776'__300 = T_SemiMetric_284 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric.d
d_d_302 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> Integer
d_d_302 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> Integer
d_d_302 T_SemiMetric_284
v0
  = case T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0 of
      C_SemiMetric'46'constructor_4991 AgdaAny -> AgdaAny -> Integer
v3 T_IsSemiMetric_250
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_SemiMetric_284
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.SemiMetric.isSemiMetric
d_isSemiMetric_304 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_250
d_isSemiMetric_304 :: T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 T_SemiMetric_284
v0
  = case T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0 of
      C_SemiMetric'46'constructor_4991 AgdaAny -> AgdaAny -> Integer
v3 T_IsSemiMetric_250
v4 -> T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v4
      T_SemiMetric_284
_ -> T_IsSemiMetric_250
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.SemiMetric._.0⇒≈
d_0'8658''8776'_308 ::
  T_SemiMetric_284 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_308 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_308 T_SemiMetric_284
v0
  = (T_IsQuasiSemiMetric_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_184
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
         ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.antisym
d_antisym_310 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_310 :: T_SemiMetric_284
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_310 = T_SemiMetric_284
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.cong
d_cong_312 ::
  T_SemiMetric_284 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_312 :: T_SemiMetric_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_312 = T_SemiMetric_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.isEquivalence
d_isEquivalence_314 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_314 :: T_SemiMetric_284 -> T_IsEquivalence_26
d_isEquivalence_314 T_SemiMetric_284
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPartialOrder
d_isPartialOrder_316 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_316 :: T_SemiMetric_284 -> T_IsPartialOrder_174
d_isPartialOrder_316 T_SemiMetric_284
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPreMetric
d_isPreMetric_318 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_102
d_isPreMetric_318 :: T_SemiMetric_284 -> T_IsPreMetric_102
d_isPreMetric_318 T_SemiMetric_284
v0
  = (T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> T_IsPreMetric_102
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
         ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.isPreorder
d_isPreorder_320 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_320 :: T_SemiMetric_284 -> T_IsPreorder_70
d_isPreorder_320 T_SemiMetric_284
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isProtoMetric
d_isProtoMetric_322 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_322 :: T_SemiMetric_284 -> T_IsProtoMetric_30
d_isProtoMetric_322 T_SemiMetric_284
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
         ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
            ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0))))
-- Function.Metric.Nat.Bundles.SemiMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_324 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_324 :: T_SemiMetric_284 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_324 T_SemiMetric_284
v0
  = (T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe
      T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
      ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0))
-- Function.Metric.Nat.Bundles.SemiMetric._.nonNegative
d_nonNegative_326 ::
  T_SemiMetric_284 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_326 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_326 T_SemiMetric_284
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.refl
d_refl_328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_328 :: () -> () -> T_SemiMetric_284 -> Integer -> T__'8804'__22
d_refl_328 ~()
v0 ~()
v1 T_SemiMetric_284
v2 = T_SemiMetric_284 -> Integer -> T__'8804'__22
du_refl_328 T_SemiMetric_284
v2
du_refl_328 ::
  T_SemiMetric_284 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_328 :: T_SemiMetric_284 -> Integer -> T__'8804'__22
du_refl_328 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.reflexive
d_reflexive_330 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_330 :: T_SemiMetric_284
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_330 T_SemiMetric_284
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.sym
d_sym_332 ::
  T_SemiMetric_284 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_332 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_332 = T_SemiMetric_284 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.trans
d_trans_334 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_334 :: T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_334 T_SemiMetric_284
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_336 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_336 :: T_SemiMetric_284 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_336 T_SemiMetric_284
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≈⇒0
d_'8776''8658'0_338 ::
  T_SemiMetric_284 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_338 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_338 = T_SemiMetric_284 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_340 :: () -> () -> T_SemiMetric_284 -> T_Σ_14
d_'8764''45'resp'45''8776'_340 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284 -> T_Σ_14
du_'8764''45'resp'45''8776'_340 T_SemiMetric_284
v2
du_'8764''45'resp'45''8776'_340 ::
  T_SemiMetric_284 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_340 :: T_SemiMetric_284 -> T_Σ_14
du_'8764''45'resp'45''8776'_340 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_342 :: ()
-> ()
-> T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_342 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_342 T_SemiMetric_284
v2
du_'8764''45'resp'691''45''8776'_342 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_342 :: T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_342 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_344 :: ()
-> ()
-> T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_344 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_344 T_SemiMetric_284
v2
du_'8764''45'resp'737''45''8776'_344 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_344 :: T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_344 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_346 :: () -> () -> T_SemiMetric_284 -> T_Σ_14
d_'8818''45'resp'45''8776'_346 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284 -> T_Σ_14
du_'8818''45'resp'45''8776'_346 T_SemiMetric_284
v2
du_'8818''45'resp'45''8776'_346 ::
  T_SemiMetric_284 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_346 :: T_SemiMetric_284 -> T_Σ_14
du_'8818''45'resp'45''8776'_346 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_348 :: ()
-> ()
-> T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_348 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_348 T_SemiMetric_284
v2
du_'8818''45'resp'691''45''8776'_348 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_348 :: T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_348 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_350 :: ()
-> ()
-> T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_350 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_350 T_SemiMetric_284
v2
du_'8818''45'resp'737''45''8776'_350 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_350 :: T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_350 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
                     ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                        (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v5)))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_354 :: () -> () -> T_SemiMetric_284 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_354 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_354 T_SemiMetric_284
v2
du_isPartialEquivalence_354 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_354 :: T_SemiMetric_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_354 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsProtoMetric_30 -> T_IsEquivalence_26
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_356 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny
d_refl_356 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny
d_refl_356 T_SemiMetric_284
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.reflexive
d_reflexive_358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_358 :: ()
-> ()
-> T_SemiMetric_284
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_358 ~()
v0 ~()
v1 T_SemiMetric_284
v2 = T_SemiMetric_284 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_358 T_SemiMetric_284
v2
du_reflexive_358 ::
  T_SemiMetric_284 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_358 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_358 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsProtoMetric_30 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsProtoMetric_30 -> T_IsEquivalence_26
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_360 ::
  T_SemiMetric_284 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_360 :: T_SemiMetric_284 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_360 T_SemiMetric_284
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.EqC.trans
d_trans_362 ::
  T_SemiMetric_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_362 :: T_SemiMetric_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_362 T_SemiMetric_284
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_SemiMetric_284 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_366 :: () -> () -> T_SemiMetric_284 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_366 ~()
v0 ~()
v1 T_SemiMetric_284
v2
  = T_SemiMetric_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_366 T_SemiMetric_284
v2
du_isPartialEquivalence_366 ::
  T_SemiMetric_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_366 :: T_SemiMetric_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_366 T_SemiMetric_284
v0
  = let v1 :: T_IsSemiMetric_250
v1 = T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiSemiMetric_174
v2
             = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                 (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreMetric_102
v3
                = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                    (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsProtoMetric_30
v4
                   = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                       (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_174
v5
                      = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                             (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))))))))
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.refl
d_refl_368 ::
  T_SemiMetric_284 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_368 :: T_SemiMetric_284 -> Integer -> T__'8801'__12
d_refl_368 = T_SemiMetric_284 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.reflexive
d_reflexive_370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_370 :: ()
-> ()
-> T_SemiMetric_284
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_370 = ()
-> ()
-> T_SemiMetric_284
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.sym
d_sym_372 ::
  T_SemiMetric_284 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_372 :: T_SemiMetric_284
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_372 = T_SemiMetric_284
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric._.Eq.trans
d_trans_374 ::
  T_SemiMetric_284 ->
  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_374 :: T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_374 = T_SemiMetric_284
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.SemiMetric.quasiSemiMetric
d_quasiSemiMetric_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 -> T_QuasiSemiMetric_186
d_quasiSemiMetric_376 :: () -> () -> T_SemiMetric_284 -> T_QuasiSemiMetric_186
d_quasiSemiMetric_376 ~()
v0 ~()
v1 T_SemiMetric_284
v2 = T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 T_SemiMetric_284
v2
du_quasiSemiMetric_376 :: T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 :: T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 T_SemiMetric_284
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsQuasiSemiMetric_174 -> T_QuasiSemiMetric_186)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsQuasiSemiMetric_174
-> T_QuasiSemiMetric_186
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsQuasiSemiMetric_174 -> T_QuasiSemiMetric_186
C_QuasiSemiMetric'46'constructor_3255 (T_SemiMetric_284 -> AgdaAny -> AgdaAny -> Integer
d_d_302 (T_SemiMetric_284 -> T_SemiMetric_284
forall a b. a -> b
coe T_SemiMetric_284
v0))
      (T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
         ((T_SemiMetric_284 -> T_IsSemiMetric_250)
-> AgdaAny -> T_IsSemiMetric_250
forall a b. a -> b
coe T_SemiMetric_284 -> T_IsSemiMetric_250
d_isSemiMetric_304 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0)))
-- Function.Metric.Nat.Bundles.SemiMetric._.preMetric
d_preMetric_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 -> T_PreMetric_96
d_preMetric_380 :: () -> () -> T_SemiMetric_284 -> T_PreMetric_96
d_preMetric_380 ~()
v0 ~()
v1 T_SemiMetric_284
v2 = T_SemiMetric_284 -> T_PreMetric_96
du_preMetric_380 T_SemiMetric_284
v2
du_preMetric_380 :: T_SemiMetric_284 -> T_PreMetric_96
du_preMetric_380 :: T_SemiMetric_284 -> T_PreMetric_96
du_preMetric_380 T_SemiMetric_284
v0
  = (T_QuasiSemiMetric_186 -> T_PreMetric_96)
-> AgdaAny -> T_PreMetric_96
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 ((T_SemiMetric_284 -> T_QuasiSemiMetric_186) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0))
-- Function.Metric.Nat.Bundles.SemiMetric._.protoMetric
d_protoMetric_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiMetric_284 -> T_ProtoMetric_12
d_protoMetric_382 :: () -> () -> T_SemiMetric_284 -> T_ProtoMetric_12
d_protoMetric_382 ~()
v0 ~()
v1 T_SemiMetric_284
v2 = T_SemiMetric_284 -> T_ProtoMetric_12
du_protoMetric_382 T_SemiMetric_284
v2
du_protoMetric_382 :: T_SemiMetric_284 -> T_ProtoMetric_12
du_protoMetric_382 :: T_SemiMetric_284 -> T_ProtoMetric_12
du_protoMetric_382 T_SemiMetric_284
v0
  = let v1 :: t
v1 = (T_SemiMetric_284 -> T_QuasiSemiMetric_186) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 (T_SemiMetric_284 -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe ((T_PreMetric_96 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_ProtoMetric_12
du_protoMetric_180 ((T_QuasiSemiMetric_186 -> T_PreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Metric.Nat.Bundles.Metric
d_Metric_388 :: p -> p -> ()
d_Metric_388 p
a0 p
a1 = ()
data T_Metric_388
  = C_Metric'46'constructor_6797 (AgdaAny -> AgdaAny -> Integer)
                                 MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_332
-- Function.Metric.Nat.Bundles.Metric.Carrier
d_Carrier_402 :: T_Metric_388 -> ()
d_Carrier_402 :: T_Metric_388 -> ()
d_Carrier_402 = T_Metric_388 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._≈_
d__'8776'__404 :: T_Metric_388 -> AgdaAny -> AgdaAny -> ()
d__'8776'__404 :: T_Metric_388 -> AgdaAny -> AgdaAny -> ()
d__'8776'__404 = T_Metric_388 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric.d
d_d_406 :: T_Metric_388 -> AgdaAny -> AgdaAny -> Integer
d_d_406 :: T_Metric_388 -> AgdaAny -> AgdaAny -> Integer
d_d_406 T_Metric_388
v0
  = case T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0 of
      C_Metric'46'constructor_6797 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_332
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_Metric_388
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.Metric.isMetric
d_isMetric_408 ::
  T_Metric_388 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_332
d_isMetric_408 :: T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 T_Metric_388
v0
  = case T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0 of
      C_Metric'46'constructor_6797 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_332
v4 -> T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v4
      T_Metric_388
_ -> T_IsGeneralMetric_332
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.Metric._.0⇒≈
d_0'8658''8776'_412 ::
  T_Metric_388 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_412 :: T_Metric_388 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_412 T_Metric_388
v0
  = (T_IsQuasiSemiMetric_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_184
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
         ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
            ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))
-- Function.Metric.Nat.Bundles.Metric._.antisym
d_antisym_414 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_414 :: T_Metric_388
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_414 = T_Metric_388
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.cong
d_cong_416 ::
  T_Metric_388 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_416 :: T_Metric_388
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_416 = T_Metric_388
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.isEquivalence
d_isEquivalence_418 ::
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_418 :: T_Metric_388 -> T_IsEquivalence_26
d_isEquivalence_418 T_Metric_388
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                        ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.isPartialOrder
d_isPartialOrder_420 ::
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_420 :: T_Metric_388 -> T_IsPartialOrder_174
d_isPartialOrder_420 T_Metric_388
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                  ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.isPreMetric
d_isPreMetric_422 ::
  T_Metric_388 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_102
d_isPreMetric_422 :: T_Metric_388 -> T_IsPreMetric_102
d_isPreMetric_422 T_Metric_388
v0
  = (T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> T_IsPreMetric_102
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
         ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
            ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))
-- Function.Metric.Nat.Bundles.Metric._.isPreorder
d_isPreorder_424 ::
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_424 :: T_Metric_388 -> T_IsPreorder_70
d_isPreorder_424 T_Metric_388
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.isProtoMetric
d_isProtoMetric_426 ::
  T_Metric_388 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_426 :: T_Metric_388 -> T_IsProtoMetric_30
d_isProtoMetric_426 T_Metric_388
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
         ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
            ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
               ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0)))))
-- Function.Metric.Nat.Bundles.Metric._.isQuasiSemiMetric
d_isQuasiSemiMetric_428 ::
  T_Metric_388 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_428 :: T_Metric_388 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_428 T_Metric_388
v0
  = (T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe
      T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
      ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
         ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0)))
-- Function.Metric.Nat.Bundles.Metric._.isSemiMetric
d_isSemiMetric_430 ::
  T_Metric_388 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_250
d_isSemiMetric_430 :: T_Metric_388 -> T_IsSemiMetric_250
d_isSemiMetric_430 T_Metric_388
v0
  = (T_IsGeneralMetric_332 -> T_IsSemiMetric_250)
-> AgdaAny -> T_IsSemiMetric_250
forall a b. a -> b
coe
      T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
      ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))
-- Function.Metric.Nat.Bundles.Metric._.nonNegative
d_nonNegative_432 ::
  T_Metric_388 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_432 :: T_Metric_388 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_432 T_Metric_388
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                  ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.refl
d_refl_434 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_434 :: () -> () -> T_Metric_388 -> Integer -> T__'8804'__22
d_refl_434 ~()
v0 ~()
v1 T_Metric_388
v2 = T_Metric_388 -> Integer -> T__'8804'__22
du_refl_434 T_Metric_388
v2
du_refl_434 ::
  T_Metric_388 -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_434 :: T_Metric_388 -> Integer -> T__'8804'__22
du_refl_434 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.reflexive
d_reflexive_436 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_436 :: T_Metric_388
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_436 T_Metric_388
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                        ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.sym
d_sym_438 ::
  T_Metric_388 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_438 :: T_Metric_388 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_438 = T_Metric_388 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.trans
d_trans_440 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_440 :: T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_440 T_Metric_388
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                        ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))))))
-- Function.Metric.Nat.Bundles.Metric._.triangle
d_triangle_442 ::
  T_Metric_388 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_triangle_442 :: T_Metric_388 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
d_triangle_442 T_Metric_388
v0
  = (T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_triangle_344
      ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))
-- Function.Metric.Nat.Bundles.Metric._.≈-isEquivalence
d_'8776''45'isEquivalence_444 ::
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_444 :: T_Metric_388 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_444 T_Metric_388
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                  ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))))))
-- Function.Metric.Nat.Bundles.Metric._.≈⇒0
d_'8776''8658'0_446 ::
  T_Metric_388 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_446 :: T_Metric_388 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_446 = T_Metric_388 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.∼-resp-≈
d_'8764''45'resp'45''8776'_448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_448 :: () -> () -> T_Metric_388 -> T_Σ_14
d_'8764''45'resp'45''8776'_448 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388 -> T_Σ_14
du_'8764''45'resp'45''8776'_448 T_Metric_388
v2
du_'8764''45'resp'45''8776'_448 ::
  T_Metric_388 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_448 :: T_Metric_388 -> T_Σ_14
du_'8764''45'resp'45''8776'_448 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_450 :: ()
-> ()
-> T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_450 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_450 T_Metric_388
v2
du_'8764''45'resp'691''45''8776'_450 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_450 :: T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_450 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_452 :: ()
-> ()
-> T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_452 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_452 T_Metric_388
v2
du_'8764''45'resp'737''45''8776'_452 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_452 :: T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_452 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.≲-resp-≈
d_'8818''45'resp'45''8776'_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_454 :: () -> () -> T_Metric_388 -> T_Σ_14
d_'8818''45'resp'45''8776'_454 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388 -> T_Σ_14
du_'8818''45'resp'45''8776'_454 T_Metric_388
v2
du_'8818''45'resp'45''8776'_454 ::
  T_Metric_388 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_454 :: T_Metric_388 -> T_Σ_14
du_'8818''45'resp'45''8776'_454 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_456 :: ()
-> ()
-> T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_456 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_456 T_Metric_388
v2
du_'8818''45'resp'691''45''8776'_456 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_456 :: T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_456 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_458 :: ()
-> ()
-> T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_458 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_458 T_Metric_388
v2
du_'8818''45'resp'737''45''8776'_458 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_458 :: T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_458 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.isPartialEquivalence
d_isPartialEquivalence_462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_462 :: () -> () -> T_Metric_388 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_462 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_462 T_Metric_388
v2
du_isPartialEquivalence_462 ::
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_462 :: T_Metric_388 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_462 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_464 :: T_Metric_388 -> AgdaAny -> AgdaAny
d_refl_464 :: T_Metric_388 -> AgdaAny -> AgdaAny
d_refl_464 T_Metric_388
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.reflexive
d_reflexive_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_466 :: ()
-> ()
-> T_Metric_388
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_466 ~()
v0 ~()
v1 T_Metric_388
v2 = T_Metric_388 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_466 T_Metric_388
v2
du_reflexive_466 ::
  T_Metric_388 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_466 :: T_Metric_388 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_466 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_468 ::
  T_Metric_388 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_468 :: T_Metric_388 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_468 T_Metric_388
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.EqC.trans
d_trans_470 ::
  T_Metric_388 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_470 :: T_Metric_388
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_470 T_Metric_388
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_Metric_388 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0)))))))
-- Function.Metric.Nat.Bundles.Metric._.Eq.isPartialEquivalence
d_isPartialEquivalence_474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_474 :: () -> () -> T_Metric_388 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_474 ~()
v0 ~()
v1 T_Metric_388
v2
  = T_Metric_388 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_474 T_Metric_388
v2
du_isPartialEquivalence_474 ::
  T_Metric_388 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_474 :: T_Metric_388 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_474 T_Metric_388
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                                (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_476 ::
  T_Metric_388 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_476 :: T_Metric_388 -> Integer -> T__'8801'__12
d_refl_476 = T_Metric_388 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.reflexive
d_reflexive_478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_478 :: ()
-> ()
-> T_Metric_388
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_478 = ()
-> ()
-> T_Metric_388
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.sym
d_sym_480 ::
  T_Metric_388 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_480 :: T_Metric_388
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_480 = T_Metric_388
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric._.Eq.trans
d_trans_482 ::
  T_Metric_388 ->
  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_482 :: T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_482 = T_Metric_388
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.Metric.semiMetric
d_semiMetric_484 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 -> T_SemiMetric_284
d_semiMetric_484 :: () -> () -> T_Metric_388 -> T_SemiMetric_284
d_semiMetric_484 ~()
v0 ~()
v1 T_Metric_388
v2 = T_Metric_388 -> T_SemiMetric_284
du_semiMetric_484 T_Metric_388
v2
du_semiMetric_484 :: T_Metric_388 -> T_SemiMetric_284
du_semiMetric_484 :: T_Metric_388 -> T_SemiMetric_284
du_semiMetric_484 T_Metric_388
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsSemiMetric_250 -> T_SemiMetric_284)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_250
-> T_SemiMetric_284
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_250 -> T_SemiMetric_284
C_SemiMetric'46'constructor_4991 (T_Metric_388 -> AgdaAny -> AgdaAny -> Integer
d_d_406 (T_Metric_388 -> T_Metric_388
forall a b. a -> b
coe T_Metric_388
v0))
      (T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
         ((T_Metric_388 -> T_IsGeneralMetric_332)
-> AgdaAny -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_Metric_388 -> T_IsGeneralMetric_332
d_isMetric_408 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0)))
-- Function.Metric.Nat.Bundles.Metric._.preMetric
d_preMetric_488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 -> T_PreMetric_96
d_preMetric_488 :: () -> () -> T_Metric_388 -> T_PreMetric_96
d_preMetric_488 ~()
v0 ~()
v1 T_Metric_388
v2 = T_Metric_388 -> T_PreMetric_96
du_preMetric_488 T_Metric_388
v2
du_preMetric_488 :: T_Metric_388 -> T_PreMetric_96
du_preMetric_488 :: T_Metric_388 -> T_PreMetric_96
du_preMetric_488 T_Metric_388
v0
  = let v1 :: t
v1 = (T_Metric_388 -> T_SemiMetric_284) -> AgdaAny -> t
forall a b. a -> b
coe T_Metric_388 -> T_SemiMetric_284
du_semiMetric_484 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> T_PreMetric_96
forall a b. a -> b
coe ((T_QuasiSemiMetric_186 -> T_PreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 ((T_SemiMetric_284 -> T_QuasiSemiMetric_186) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Metric.Nat.Bundles.Metric._.protoMetric
d_protoMetric_490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 -> T_ProtoMetric_12
d_protoMetric_490 :: () -> () -> T_Metric_388 -> T_ProtoMetric_12
d_protoMetric_490 ~()
v0 ~()
v1 T_Metric_388
v2 = T_Metric_388 -> T_ProtoMetric_12
du_protoMetric_490 T_Metric_388
v2
du_protoMetric_490 :: T_Metric_388 -> T_ProtoMetric_12
du_protoMetric_490 :: T_Metric_388 -> T_ProtoMetric_12
du_protoMetric_490 T_Metric_388
v0
  = let v1 :: t
v1 = (T_Metric_388 -> T_SemiMetric_284) -> AgdaAny -> t
forall a b. a -> b
coe T_Metric_388 -> T_SemiMetric_284
du_semiMetric_484 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiMetric_284 -> T_QuasiSemiMetric_186) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_PreMetric_96 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_ProtoMetric_12
du_protoMetric_180 ((T_QuasiSemiMetric_186 -> T_PreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Metric.Nat.Bundles.Metric._.quasiSemiMetric
d_quasiSemiMetric_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Metric_388 -> T_QuasiSemiMetric_186
d_quasiSemiMetric_492 :: () -> () -> T_Metric_388 -> T_QuasiSemiMetric_186
d_quasiSemiMetric_492 ~()
v0 ~()
v1 T_Metric_388
v2 = T_Metric_388 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_492 T_Metric_388
v2
du_quasiSemiMetric_492 :: T_Metric_388 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_492 :: T_Metric_388 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_492 T_Metric_388
v0
  = (T_SemiMetric_284 -> T_QuasiSemiMetric_186)
-> AgdaAny -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 ((T_Metric_388 -> T_SemiMetric_284) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Metric_388 -> T_SemiMetric_284
du_semiMetric_484 (T_Metric_388 -> AgdaAny
forall a b. a -> b
coe T_Metric_388
v0))
-- Function.Metric.Nat.Bundles.UltraMetric
d_UltraMetric_498 :: p -> p -> ()
d_UltraMetric_498 p
a0 p
a1 = ()
data T_UltraMetric_498
  = C_UltraMetric'46'constructor_8503 (AgdaAny -> AgdaAny -> Integer)
                                      MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_332
-- Function.Metric.Nat.Bundles.UltraMetric.Carrier
d_Carrier_512 :: T_UltraMetric_498 -> ()
d_Carrier_512 :: T_UltraMetric_498 -> ()
d_Carrier_512 = T_UltraMetric_498 -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._≈_
d__'8776'__514 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> ()
d__'8776'__514 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> ()
d__'8776'__514 = T_UltraMetric_498 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric.d
d_d_516 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> Integer
d_d_516 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> Integer
d_d_516 T_UltraMetric_498
v0
  = case T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0 of
      C_UltraMetric'46'constructor_8503 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_332
v4 -> (AgdaAny -> AgdaAny -> Integer) -> AgdaAny -> AgdaAny -> Integer
forall a b. a -> b
coe AgdaAny -> AgdaAny -> Integer
v3
      T_UltraMetric_498
_ -> AgdaAny -> AgdaAny -> Integer
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.UltraMetric.isUltraMetric
d_isUltraMetric_518 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_332
d_isUltraMetric_518 :: T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 T_UltraMetric_498
v0
  = case T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0 of
      C_UltraMetric'46'constructor_8503 AgdaAny -> AgdaAny -> Integer
v3 T_IsGeneralMetric_332
v4 -> T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v4
      T_UltraMetric_498
_ -> T_IsGeneralMetric_332
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Metric.Nat.Bundles.UltraMetric._.0⇒≈
d_0'8658''8776'_522 ::
  T_UltraMetric_498 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_0'8658''8776'_522 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
d_0'8658''8776'_522 T_UltraMetric_498
v0
  = (T_IsQuasiSemiMetric_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_0'8658''8776'_184
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
         ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
            ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))
-- Function.Metric.Nat.Bundles.UltraMetric._.antisym
d_antisym_524 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antisym_524 :: T_UltraMetric_498
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
d_antisym_524 = T_UltraMetric_498
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.cong
d_cong_526 ::
  T_UltraMetric_498 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_cong_526 :: T_UltraMetric_498
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
d_cong_526 = T_UltraMetric_498
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.isEquivalence
d_isEquivalence_528 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_528 :: T_UltraMetric_498 -> T_IsEquivalence_26
d_isEquivalence_528 T_UltraMetric_498
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                        ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPartialOrder
d_isPartialOrder_530 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_530 :: T_UltraMetric_498 -> T_IsPartialOrder_174
d_isPartialOrder_530 T_UltraMetric_498
v0
  = (T_IsProtoMetric_30 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                  ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPreMetric
d_isPreMetric_532 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_102
d_isPreMetric_532 :: T_UltraMetric_498 -> T_IsPreMetric_102
d_isPreMetric_532 T_UltraMetric_498
v0
  = (T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> T_IsPreMetric_102
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
      ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
         ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
            ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isPreorder
d_isPreorder_534 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_534 :: T_UltraMetric_498 -> T_IsPreorder_70
d_isPreorder_534 T_UltraMetric_498
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
         ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isProtoMetric
d_isProtoMetric_536 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_isProtoMetric_536 :: T_UltraMetric_498 -> T_IsProtoMetric_30
d_isProtoMetric_536 T_UltraMetric_498
v0
  = (T_IsPreMetric_102 -> T_IsProtoMetric_30)
-> AgdaAny -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
      ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
         ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
            ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
               ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0)))))
-- Function.Metric.Nat.Bundles.UltraMetric._.isQuasiSemiMetric
d_isQuasiSemiMetric_538 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_538 :: T_UltraMetric_498 -> T_IsQuasiSemiMetric_174
d_isQuasiSemiMetric_538 T_UltraMetric_498
v0
  = (T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe
      T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
      ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
         ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0)))
-- Function.Metric.Nat.Bundles.UltraMetric._.isSemiMetric
d_isSemiMetric_540 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_250
d_isSemiMetric_540 :: T_UltraMetric_498 -> T_IsSemiMetric_250
d_isSemiMetric_540 T_UltraMetric_498
v0
  = (T_IsGeneralMetric_332 -> T_IsSemiMetric_250)
-> AgdaAny -> T_IsSemiMetric_250
forall a b. a -> b
coe
      T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
      ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))
-- Function.Metric.Nat.Bundles.UltraMetric._.nonNegative
d_nonNegative_542 ::
  T_UltraMetric_498 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_nonNegative_542 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> T__'8804'__22
d_nonNegative_542 T_UltraMetric_498
v0
  = (T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsProtoMetric_30 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_nonNegative_48
      ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                  ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.refl
d_refl_544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_refl_544 :: () -> () -> T_UltraMetric_498 -> Integer -> T__'8804'__22
d_refl_544 ~()
v0 ~()
v1 T_UltraMetric_498
v2 = T_UltraMetric_498 -> Integer -> T__'8804'__22
du_refl_544 T_UltraMetric_498
v2
du_refl_544 ::
  T_UltraMetric_498 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_refl_544 :: T_UltraMetric_498 -> Integer -> T__'8804'__22
du_refl_544 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.reflexive
d_reflexive_546 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_reflexive_546 :: T_UltraMetric_498
-> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_reflexive_546 T_UltraMetric_498
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                        ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.sym
d_sym_548 ::
  T_UltraMetric_498 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_548 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> T__'8801'__12
d_sym_548 = T_UltraMetric_498 -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.trans
d_trans_550 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_trans_550 :: T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_trans_550 T_UltraMetric_498
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsProtoMetric_30 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsProtoMetric_30 -> T_IsPartialOrder_174
MAlonzo.Code.Function.Metric.Structures.d_isPartialOrder_42
            ((T_IsPreMetric_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
               ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                  ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                     ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                        ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.triangle
d_triangle_552 ::
  T_UltraMetric_498 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_triangle_552 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
d_triangle_552 T_UltraMetric_498
v0
  = (T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8804'__22
forall a b. a -> b
coe
      T_IsGeneralMetric_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Metric.Structures.d_triangle_344
      ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))
-- Function.Metric.Nat.Bundles.UltraMetric._.≈-isEquivalence
d_'8776''45'isEquivalence_554 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_'8776''45'isEquivalence_554 :: T_UltraMetric_498 -> T_IsEquivalence_26
d_'8776''45'isEquivalence_554 T_UltraMetric_498
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
         ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
            ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
               ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                  ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≈⇒0
d_'8776''8658'0_556 ::
  T_UltraMetric_498 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8776''8658'0_556 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
d_'8776''8658'0_556 = T_UltraMetric_498 -> AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-resp-≈
d_'8764''45'resp'45''8776'_558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_558 :: () -> () -> T_UltraMetric_498 -> T_Σ_14
d_'8764''45'resp'45''8776'_558 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498 -> T_Σ_14
du_'8764''45'resp'45''8776'_558 T_UltraMetric_498
v2
du_'8764''45'resp'45''8776'_558 ::
  T_UltraMetric_498 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_558 :: T_UltraMetric_498 -> T_Σ_14
du_'8764''45'resp'45''8776'_558 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_118
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'691''45''8776'_560 :: ()
-> ()
-> T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'691''45''8776'_560 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_560 T_UltraMetric_498
v2
du_'8764''45'resp'691''45''8776'_560 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'691''45''8776'_560 :: T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'691''45''8776'_560 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_116
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8764''45'resp'737''45''8776'_562 :: ()
-> ()
-> T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8764''45'resp'737''45''8776'_562 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_562 T_UltraMetric_498
v2
du_'8764''45'resp'737''45''8776'_562 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8764''45'resp'737''45''8776'_562 :: T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8764''45'resp'737''45''8776'_562 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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'_114
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≲-resp-≈
d_'8818''45'resp'45''8776'_564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_564 :: () -> () -> T_UltraMetric_498 -> T_Σ_14
d_'8818''45'resp'45''8776'_564 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498 -> T_Σ_14
du_'8818''45'resp'45''8776'_564 T_UltraMetric_498
v2
du_'8818''45'resp'45''8776'_564 ::
  T_UltraMetric_498 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_564 :: T_UltraMetric_498 -> T_Σ_14
du_'8818''45'resp'45''8776'_564 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'45''8776'_112
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'691''45''8776'_566 :: ()
-> ()
-> T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'691''45''8776'_566 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_566 T_UltraMetric_498
v2
du_'8818''45'resp'691''45''8776'_566 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'691''45''8776'_566 :: T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'691''45''8776'_566 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'691''45''8776'_106
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8818''45'resp'737''45''8776'_568 :: ()
-> ()
-> T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
d_'8818''45'resp'737''45''8776'_568 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_568 T_UltraMetric_498
v2
du_'8818''45'resp'737''45''8776'_568 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8818''45'resp'737''45''8776'_568 :: T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
du_'8818''45'resp'737''45''8776'_568 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_'8818''45'resp'737''45''8776'_100
                        ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                           (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v6))))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.isPartialEquivalence
d_isPartialEquivalence_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_572 :: () -> () -> T_UltraMetric_498 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_572 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_572 T_UltraMetric_498
v2
du_isPartialEquivalence_572 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_572 :: T_UltraMetric_498 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_572 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_574 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny
d_refl_574 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny
d_refl_574 T_UltraMetric_498
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.reflexive
d_reflexive_576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_576 :: ()
-> ()
-> T_UltraMetric_498
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_576 ~()
v0 ~()
v1 T_UltraMetric_498
v2 = T_UltraMetric_498 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_576 T_UltraMetric_498
v2
du_reflexive_576 ::
  T_UltraMetric_498 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_576 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_576 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
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_578 ::
  T_UltraMetric_498 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_578 :: T_UltraMetric_498 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_578 T_UltraMetric_498
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.EqC.trans
d_trans_580 ::
  T_UltraMetric_498 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_580 :: T_UltraMetric_498
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_580 T_UltraMetric_498
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_102 -> T_IsProtoMetric_30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
            ((T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
               ((T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                  ((T_IsGeneralMetric_332 -> T_IsSemiMetric_250) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                     ((T_UltraMetric_498 -> T_IsGeneralMetric_332) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0)))))))
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.isPartialEquivalence
d_isPartialEquivalence_584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_584 :: () -> () -> T_UltraMetric_498 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_584 ~()
v0 ~()
v1 T_UltraMetric_498
v2
  = T_UltraMetric_498 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_584 T_UltraMetric_498
v2
du_isPartialEquivalence_584 ::
  T_UltraMetric_498 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_584 :: T_UltraMetric_498 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_584 T_UltraMetric_498
v0
  = let v1 :: T_IsGeneralMetric_332
v1 = T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiMetric_250
v2
             = T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
                 (T_IsGeneralMetric_332 -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_IsGeneralMetric_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasiSemiMetric_174
v3
                = T_IsSemiMetric_250 -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.d_isQuasiSemiMetric_258
                    (T_IsSemiMetric_250 -> T_IsSemiMetric_250
forall a b. a -> b
coe T_IsSemiMetric_250
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreMetric_102
v4
                   = T_IsQuasiSemiMetric_174 -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.d_isPreMetric_182
                       (T_IsQuasiSemiMetric_174 -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsProtoMetric_30
v5
                      = T_IsPreMetric_102 -> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.d_isProtoMetric_110
                          (T_IsPreMetric_102 -> T_IsPreMetric_102
forall a b. a -> b
coe T_IsPreMetric_102
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPartialOrder_174
v6
                         = T_IsProtoMetric_30 -> T_IsPartialOrder_174
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_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                                (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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_586 ::
  T_UltraMetric_498 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_586 :: T_UltraMetric_498 -> Integer -> T__'8801'__12
d_refl_586 = T_UltraMetric_498 -> Integer -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.reflexive
d_reflexive_588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_588 :: ()
-> ()
-> T_UltraMetric_498
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_588 = ()
-> ()
-> T_UltraMetric_498
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.sym
d_sym_590 ::
  T_UltraMetric_498 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_590 :: T_UltraMetric_498
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sym_590 = T_UltraMetric_498
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric._.Eq.trans
d_trans_592 ::
  T_UltraMetric_498 ->
  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_592 :: T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_592 = T_UltraMetric_498
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Function.Metric.Nat.Bundles.UltraMetric.semiMetric
d_semiMetric_594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 -> T_SemiMetric_284
d_semiMetric_594 :: () -> () -> T_UltraMetric_498 -> T_SemiMetric_284
d_semiMetric_594 ~()
v0 ~()
v1 T_UltraMetric_498
v2 = T_UltraMetric_498 -> T_SemiMetric_284
du_semiMetric_594 T_UltraMetric_498
v2
du_semiMetric_594 :: T_UltraMetric_498 -> T_SemiMetric_284
du_semiMetric_594 :: T_UltraMetric_498 -> T_SemiMetric_284
du_semiMetric_594 T_UltraMetric_498
v0
  = ((AgdaAny -> AgdaAny -> Integer)
 -> T_IsSemiMetric_250 -> T_SemiMetric_284)
-> (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_250
-> T_SemiMetric_284
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> Integer)
-> T_IsSemiMetric_250 -> T_SemiMetric_284
C_SemiMetric'46'constructor_4991 (T_UltraMetric_498 -> AgdaAny -> AgdaAny -> Integer
d_d_516 (T_UltraMetric_498 -> T_UltraMetric_498
forall a b. a -> b
coe T_UltraMetric_498
v0))
      (T_IsGeneralMetric_332 -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.d_isSemiMetric_342
         ((T_UltraMetric_498 -> T_IsGeneralMetric_332)
-> AgdaAny -> T_IsGeneralMetric_332
forall a b. a -> b
coe T_UltraMetric_498 -> T_IsGeneralMetric_332
d_isUltraMetric_518 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0)))
-- Function.Metric.Nat.Bundles.UltraMetric._.preMetric
d_preMetric_598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 -> T_PreMetric_96
d_preMetric_598 :: () -> () -> T_UltraMetric_498 -> T_PreMetric_96
d_preMetric_598 ~()
v0 ~()
v1 T_UltraMetric_498
v2 = T_UltraMetric_498 -> T_PreMetric_96
du_preMetric_598 T_UltraMetric_498
v2
du_preMetric_598 :: T_UltraMetric_498 -> T_PreMetric_96
du_preMetric_598 :: T_UltraMetric_498 -> T_PreMetric_96
du_preMetric_598 T_UltraMetric_498
v0
  = let v1 :: t
v1 = (T_UltraMetric_498 -> T_SemiMetric_284) -> AgdaAny -> t
forall a b. a -> b
coe T_UltraMetric_498 -> T_SemiMetric_284
du_semiMetric_594 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> T_PreMetric_96
forall a b. a -> b
coe ((T_QuasiSemiMetric_186 -> T_PreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 ((T_SemiMetric_284 -> T_QuasiSemiMetric_186) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Metric.Nat.Bundles.UltraMetric._.protoMetric
d_protoMetric_600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 -> T_ProtoMetric_12
d_protoMetric_600 :: () -> () -> T_UltraMetric_498 -> T_ProtoMetric_12
d_protoMetric_600 ~()
v0 ~()
v1 T_UltraMetric_498
v2 = T_UltraMetric_498 -> T_ProtoMetric_12
du_protoMetric_600 T_UltraMetric_498
v2
du_protoMetric_600 :: T_UltraMetric_498 -> T_ProtoMetric_12
du_protoMetric_600 :: T_UltraMetric_498 -> T_ProtoMetric_12
du_protoMetric_600 T_UltraMetric_498
v0
  = let v1 :: t
v1 = (T_UltraMetric_498 -> T_SemiMetric_284) -> AgdaAny -> t
forall a b. a -> b
coe T_UltraMetric_498 -> T_SemiMetric_284
du_semiMetric_594 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0) in
    AgdaAny -> T_ProtoMetric_12
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiMetric_284 -> T_QuasiSemiMetric_186) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_PreMetric_96 -> T_ProtoMetric_12) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_PreMetric_96 -> T_ProtoMetric_12
du_protoMetric_180 ((T_QuasiSemiMetric_186 -> T_PreMetric_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_QuasiSemiMetric_186 -> T_PreMetric_96
du_preMetric_274 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Metric.Nat.Bundles.UltraMetric._.quasiSemiMetric
d_quasiSemiMetric_602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UltraMetric_498 -> T_QuasiSemiMetric_186
d_quasiSemiMetric_602 :: () -> () -> T_UltraMetric_498 -> T_QuasiSemiMetric_186
d_quasiSemiMetric_602 ~()
v0 ~()
v1 T_UltraMetric_498
v2 = T_UltraMetric_498 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_602 T_UltraMetric_498
v2
du_quasiSemiMetric_602 ::
  T_UltraMetric_498 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_602 :: T_UltraMetric_498 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_602 T_UltraMetric_498
v0
  = (T_SemiMetric_284 -> T_QuasiSemiMetric_186)
-> AgdaAny -> T_QuasiSemiMetric_186
forall a b. a -> b
coe T_SemiMetric_284 -> T_QuasiSemiMetric_186
du_quasiSemiMetric_376 ((T_UltraMetric_498 -> T_SemiMetric_284) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498 -> T_SemiMetric_284
du_semiMetric_594 (T_UltraMetric_498 -> AgdaAny
forall a b. a -> b
coe T_UltraMetric_498
v0))