proposition: Lemma inject_Qred_ap (x y: Q): Qred x <> Qred y -> ' x >< ' y.
proof: Proof. Proof with auto. intro. apply Qap_CRap. intro. apply H. apply Qred_complete... Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QposMinMax Coq.setoid_ring.Ring_theory Coq.Setoids.Setoid Coq.QArith.QArith Coq.QArith.Qabs Coq.QArith.Qround CoRN.model.reals.CRreal CoRN.metric2.Complete CoRN.reals.fast.CRFieldOps CoRN.model.rings.Qring CoRN.algebra.CRing_Homomorphisms CoRN.model.metric2.Qmetric CoRN.tactics.CornTac CoRN.logic.Stability Coq.Logic.ConstructiveEpsilon CoRN.util.Qdlog MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders CRArith