proposition: Lemma IR_eq_as_CR : forall x y, x[=]y <-> (IRasCR x == IRasCR y)%CR.
proof: Proof. split. apply (map_wd_unfolded _ _ (iso_map_rht _ _ CRIR_iso)). intros H. stepl (CRasIR (IRasCR x)); [| now apply IRasCRasIR_id]. stepr (CRasIR (IRasCR y)); [| now apply IRasCRasIR_id]. apply map_wd_unfolded. 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