proposition: Lemma CR_lt_as_Cauchy_IR_lt_2 : forall (x y:CR), (CRasCauchy_IR x)[<](CRasCauchy_IR y) -> (x < y)%CR.
proof: Proof. intros x y H. eapply CRltT_wd;try apply CRasCR. apply Cauchy_IR_lt_as_CR_lt_1. assumption. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QposMinMax CoRN.model.reals.Cauchy_IR CoRN.tactics.CornTac Coq(Lia) CoRN.model.metric2.Qmetric CoRN.model.totalorder.QMinMax Coq.QArith.Qabs CoRN.reals.fast.CRFieldOps