(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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 Rle_min_compat_r : forall x y z, x <= y -> Rmin x z <= Rmin y z.