proposition: Lemma IR_Lim_as_CR : forall (x:CauchySeq IR), (IRasCR (Lim x)==Lim (Build_CauchySeq _ _ (IR_Cauchy_prop_as_CR x)))%CR.
proof: Proof. intros x. apply (SeqLimit_unique CRasCReals). apply (map_pres_Lim _ _ (iso_map_rht CRasCReals IR CRIR_iso) _ _ (Cauchy_complete x)). 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