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

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

Lemma Rmin_case_strong : forall r1 r2 (P:R -> Type), (r1 <= r2 -> P r1) -> (r2 <= r1 -> P r2) -> P (Rmin r1 r2).