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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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Require Export Rbase.
Require Export QArith_base.
(** Injection of rational numbers into real numbers. *)
Definition Q2R (x : Q) : R := (IZR (Qnum x) * / IZR (QDen x))%R.
Hint Resolve IZR_nz Rmult_integral_contrapositive : core.

Lemma Qlt_Rlt : forall x y : Q, x<y -> (Q2R x < Q2R y)%R.