Require Export TopologicalSpaces.
Require Export OrderTopology.
Require Export Reals.
Definition RTop := OrderTopology Rle.
Require Export MetricSpaces.
Definition R_metric (x y:R) : R := Rabs (y-x).

Lemma Rmetric_bound: forall x y z:R, R_metric x z < y - x ->
z < y.