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Added lemmas in math-classes and proved that functions between metric…
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… spaced form a metric space w.r.t. the supremum distance
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EvgenyMakarov committed Dec 18, 2012
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4 changes: 2 additions & 2 deletions broken/metric.v
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Require Import
QArith
theory.setoids (* Equiv Prop *) theory.products
stdlib_rationals (*Qinf*) Qpossec (*QposInf*) (*QnonNeg*) abstract_algebra QType_rationals additional_operations.
stdlib_rationals Qinf (*Qpossec QposInf QnonNeg*) abstract_algebra QType_rationals additional_operations.
(*Import (*QnonNeg.notations*) QArith.*)
Require Import Qauto QOrderedType.
(*Require Import orders.*)
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+ intros e e_neg f g A. specialize (A x0). eapply mspc_negative; eauto.
+ intros e e_nonneg f x; now apply mspc_refl.
+ intros e f g A x; now apply mspc_symm.
+ intros e1 e2 f g h A1 A2 x. now apply mspc_triangle with (b := g x).
+ intros e1 e2 f g h A1 A2 x. now apply mspc_triangle with (b := map g x).
+ intros e f g A x. apply mspc_closed; intros d A1. now apply A.
Qed.

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