proposition: Lemma CR_inv_as_Cauchy_IR_inv : forall (x:CR) x_ H, f_rcpcl (CRasCauchy_IR x) H [=] CRasCauchy_IR (@CRinvT x x_).
proof: Proof. intros x x_ H. stepl (CRasCauchy_IR (Cauchy_IRasCR (f_rcpcl (CRasCauchy_IR x) H))); [| apply Cauchy_IRasCauchy_IR]. apply CRasCauchy_IR_wd. rewrite <- Cauchy_IR_inv_as_CR_inv_short. apply CRinvT_wd. apply CRasCR. 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