proposition: Lemma Qle_CRle (x y: CR): (forall x' y', ' x' <= x -> y <= ' y' -> (x' <= y')%Q) <-> x <= y.
proof: Proof. Proof with auto. split; intros. apply (proj1 (Qle_CRle_l _ _)). intros. apply (proj1 (Qle_CRle_r _ _)). intros. apply CRle_Qle... apply CRle_Qle. apply CRle_trans with x... apply CRle_trans with y... Qed.
imports: CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QMinMax CoRN.model.totalorder.QposMinMax Coq.setoid_ring.Ring_theory Coq.Setoids.Setoid Coq.QArith.QArith Coq.QArith.Qabs Coq.QArith.Qround CoRN.metric2.Complete CoRN.metric2.ProductMetric CoRN.reals.fast.CRFieldOps CoRN.model.metric2.Qmetric CoRN.logic.Stability Coq.Logic.ConstructiveEpsilon CoRN.util.Qdlog MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders