proposition: Lemma Cauchy_IR_ap_as_CR_ap_1 : forall (x y:Cauchy_IR), x[#]y -> (CRapartT (Cauchy_IRasCR x) (Cauchy_IRasCR y))%CR.
proof: Proof. intros x y [H|H];[left|right];apply Cauchy_IR_lt_as_CR_lt_1; apply H. Defined.
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