proposition: Lemma CRltT_wd : forall x1 x2, (x1==x2 -> forall y1 y2, y1==y2 -> x1 < y1 -> x2 < y2)%CR.
proof: Proof. intros x1 x2 Hx y1 y2 Hy H. refine (CRpos_wd _ _). 2:apply H. abstract ( rewrite <- Hx; rewrite <- Hy; reflexivity ). Defined.
imports: CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QposMinMax CoRN.model.lattice.CRlattice CoRN.model.totalorder.QMinMax Coq.QArith.Qabs CoRN.model.metric2.Qmetric CoRN.metric2.ProductMetric MathClasses.interfaces.canonical_names