Notation "0" := rO.Notation "1" := rI.Notation "x + y" := (rplus x y).Notation "x * y " := (rtimes x y).Notation "x - y " := (rminus x y).Notation "- x" := (ropp x).Notation "x == y" := (req x y).Notation "x ~= y" := (~ req x y).Notation "x <= y" := (rle x y).Notation "x < y" := (rlt x y).

(* Specifications: *)
Lemma req_refl : forall x, req x x.
Lemma req_sym : forall x y, req x y -> req y x.
Lemma req_trans : forall x y z, req x y -> req y z -> req x z.