proposition: Lemma CR_plus_as_Cauchy_IR_plus : forall x y:CR, CRasCauchy_IR x [+] CRasCauchy_IR y [=] CRasCauchy_IR (x+y)%CR.
proof: Proof. apply reverse_iso_bin_uc_fun. apply Cauchy_IR_plus_as_CR_plus. 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