proposition: Lemma CR_ap_as_Cauchy_IR_ap_2 : forall (x y:CR), (CRasCauchy_IR x) [#] (CRasCauchy_IR y) -> CRapartT x y.
proof: Proof. intros x y [H|H];[left|right];apply CR_lt_as_Cauchy_IR_lt_2; 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