proposition: Lemma Cauchy_IR_eq_as_CR_eq : forall (x y:Cauchy_IR), ((Cauchy_IRasCR x) == (Cauchy_IRasCR y))%CR <-> x[=]y.
proof: Proof. intros x y. split;[|apply Cauchy_IRasCR_wd]. intros H. stepl (CRasCauchy_IR (Cauchy_IRasCR x)); [| apply Cauchy_IRasCauchy_IR]. stepr (CRasCauchy_IR (Cauchy_IRasCR y)); [| apply Cauchy_IRasCauchy_IR]. apply CRasCauchy_IR_wd. 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