Definition RTop := OrderTopology Rle.Definition R_metric (x y:R) : R := Rabs (y-x).

(* Specifications: *)
Lemma R_metric_is_metric: metric R_metric.
Lemma Rmetric_bound: forall x y z:R, R_metric x z < y - x -> z < y.
Lemma Rmetric_bound2: forall x y z:R, R_metric y z < y - x -> x < z.
Lemma RTop_metrization: metrizes RTop R_metric.