fix(library/theories/analysis/metric_space): minor correction

This commit is contained in:
Leonardo de Moura 2015-10-13 15:11:41 -07:00
parent fa937395d9
commit 9fb59a05f5

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@ -6,7 +6,7 @@ Author: Jeremy Avigad
Metric spaces.
-/
import data.real.division
open real eq.ops classical
open real eq.ops classical algebra
structure metric_space [class] (M : Type) : Type :=
(dist : M → M → )
@ -27,7 +27,7 @@ iff.intro eq_of_dist_eq_zero (suppose x = y, this ▸ !dist_self)
proposition dist_nonneg (x y : M) : 0 ≤ dist x y :=
have dist x y + dist y x ≥ 0, by rewrite -(dist_self x); apply dist_triangle,
have 2 * dist x y ≥ 0, using this,
by rewrite [-real.one_add_one, right_distrib, +one_mul, dist_comm at {2}]; apply this,
by krewrite [-real.one_add_one, right_distrib, +one_mul, dist_comm at {2}]; apply this,
nonneg_of_mul_nonneg_left this two_pos
proposition dist_pos_of_ne {x y : M} (H : x ≠ y) : dist x y > 0 :=