proposition: Lemma CR_ap_as_IR : forall x y, (IRasCR x >< IRasCR y -> x[#]y)%CR.
proof: Proof. intros. stepl (CRasIR (IRasCR x)); [| now apply IRasCRasIR_id]. stepr (CRasIR (IRasCR y)); [| now apply IRasCRasIR_id]. apply map_pres_apartness. assumption. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.CauchySeq CoRN.reals.iso_CReals CoRN.reals.R_morphism CoRN.reals.fast.CRArith CoRN.model.reals.CRreal CoRN.tactics.CornTac