(*******************************)
(** *        Rmax              *)
(*******************************)
(*********)

(* Specifications: *)
(*********)
Lemma Rmax_case : forall r1 r2 (P:R -> Type), P r1 -> P r2 -> P (Rmax r1 r2).
(*********)
Lemma Rmax_case_strong : forall r1 r2 (P:R -> Type),
(r2 <= r1 -> P r1) -> (r1 <= r2 -> P r2) -> P (Rmax r1 r2).
(*********)
Lemma Rmax_Rle : forall r1 r2 r, r <= Rmax r1 r2 <-> r <= r1 \/ r <= r2.
Lemma Rmax_comm : forall x y:R, Rmax x y = Rmax y x.
Notation RmaxSym := Rmax_comm (only parsing).