proposition: Lemma Rmetric_bound2: forall x y z:R, R_metric y z < y - x -> x < z.
proof: Proof. intros. replace z with (y + (z-y)) by ring. cut (y - z <= R_metric y z). - lra. - rewrite (metric_sym _ _ R_metric_is_metric). apply Rle_abs. Qed.
imports: TopologicalSpaces OrderTopology MetricSpaces Coq(Lra Lia) ZornsLemma(EnsemblesTactics FiniteIntersections) RationalsInReals