proposition: Lemma CR_nonZero_as_Cauchy_IR_nonZero_1 : forall (x:CR), (CRapartT x 0)%CR -> Dom (f_rcpcl' _) (CRasCauchy_IR x).
proof: Proof. intros x x_. change ((CRasCauchy_IR x)[#][0]). stepr (CRasCauchy_IR 0%CR). apply CR_ap_as_Cauchy_IR_ap_1. assumption. eapply CR_inject_Q_as_Cauchy_IR_inject_Q. 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