proposition: Lemma CR_le_as_Cauchy_IR_le : forall (x y:CR), CRasCauchy_IR x[<=]CRasCauchy_IR y <-> (x<=y)%CR.
proof: Proof. intros x y. rewrite <- Cauchy_IR_le_as_CR_le. do 2 rewrite -> CRasCR. reflexivity. 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