proposition: Lemma Cauchy_IR_nonZero_as_CR_nonZero_1 : forall (x:Cauchy_IR), Dom (f_rcpcl' _) x -> (CRapartT (Cauchy_IRasCR x) 0)%CR.
proof: Proof. intros x x_. eapply CRapartT_wd. reflexivity. symmetry. apply Cauchy_IR_inject_Q_as_CR_inject_Q. apply Cauchy_IR_ap_as_CR_ap_1. assumption. Defined.
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