proposition: Lemma Qap_CRap : forall (x y:Q), (~(x==y))%Q -> (' x)><(' y).
proof: Proof. intros x y Hxy. destruct (Q_dec x y) as [[H|H]|H]; try contradiction; destruct (Qpos_sub _ _ H) as [c Hc];[left|right]; exists c; abstract (rewrite -> CRminus_Qminus; rewrite -> CRle_Qle; rewrite -> Hc; ring_simplify; apply Qle_refl). Defined.
imports: CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QMinMax CoRN.model.totalorder.QposMinMax Coq.setoid_ring.Ring_theory Coq.Setoids.Setoid Coq.QArith.QArith Coq.QArith.Qabs Coq.QArith.Qround CoRN.metric2.Complete CoRN.metric2.ProductMetric CoRN.reals.fast.CRFieldOps CoRN.model.metric2.Qmetric CoRN.logic.Stability Coq.Logic.ConstructiveEpsilon CoRN.util.Qdlog MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders