Implicit Type r : R.(*******************************)
(** *        Rmin              *)
(*******************************)

(*********)
Definition Rmin (x y:R) : R :=
  match Rle_dec x y with
    | left _ => x
    | right _ => y
  end.

Lemma Rmin_Rgt : forall r1 r2 r, Rmin r1 r2 > r <-> r1 > r /\ r2 > r.