proposition: Lemma Cauchy_IR_ap_as_CR_ap_2 : forall (x y:Cauchy_IR), (CRapartT (Cauchy_IRasCR x) (Cauchy_IRasCR y))%CR -> x[#]y.
proof: Proof. intros x y [H|H];[left|right];apply Cauchy_IR_lt_as_CR_lt_2; apply H. 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