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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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(* This file continues Rdefinitions, with more properties of the classical reals, including the existence of least upper bounds for non-empty and bounded subsets. The name "Raxioms" and its contents are kept for backward compatibility, when the classical reals were axiomatized. Otherwise we would have merged this file into RIneq. *)
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(**    Lifts of basic operations for classical reals     *)
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Require Export ZArith_base.
Require Export Rdefinitions.
Local Open Scope R_scope.
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(** *            Field operations                        *)
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(** **   Addition                                        *)
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Open Scope CReal_scope.

Lemma Rrepr_le : forall x y:R, (x <= y)%R <-> Rrepr x <= Rrepr y.