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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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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 Rlt_Qlt : forall x y : Q, (Q2R x < Q2R y)%R -> x<y.