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