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

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

Lemma Rmin_pos : forall x y:R, 0 < x -> 0 < y -> 0 < Rmin x y.