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(*         *      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)         *)
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Local Ltac Tauto.intuition_solver ::= auto with real.
(** * Maximum and Minimum of two real numbers *)
Local Open Scope R_scope.
(** The functions [Rmax] and [Rmin] implement indeed a maximum and a minimum *)

(* Specifications: *)
Lemma Rmax_l : forall x y, y<=x -> Rmax x y = x.
Lemma Rmax_r : forall x y, x<=y -> Rmax x y = y.
Lemma Rmin_l : forall x y, x<=y -> Rmin x y = x.
Lemma Rmin_r : forall x y, y<=x -> Rmin x y = y.
Module RHasMinMax <: HasMinMax R_as_OT.