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(*         *   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)         *)
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(**          Complements for the real numbers            *)
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Local Open Scope R_scope.
Implicit Type r : R.
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(** *        Rmin              *)
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Definition Rmin (x y:R) : R :=
match Rle_dec x y with
| left _ => x
| right _ => y
end.
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(** *        Rmax              *)
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Definition Rmax (x y:R) : R :=
match Rle_dec x y with
| left _ => y
| right _ => x
end.

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