proposition: Lemma Cauchy_IR_inv_as_CR_inv : forall (x:Cauchy_IR) x_ H, (@CRinvT (Cauchy_IRasCR x) H == Cauchy_IRasCR (f_rcpcl x x_))%CR.
proof: Proof. intros x x_ H. rewrite <- Cauchy_IR_inv_as_CR_inv_short. apply CRinvT_irrelevant. 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