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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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(**          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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Lemma Rmin_Rgt : forall r1 r2 r, Rmin r1 r2 > r <-> r1 > r /\ r2 > r.