(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
(*********************************************************)
(**          Complements for the real numbers            *)
(*                                                       *)
(*********************************************************)
Local Open Scope R_scope.
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.