proposition: Lemma CRpos_nonNeg : forall x, CRpos x -> CRnonNeg x.
proof: Proof. intros x [c Hx]. cut (0 <= x)%CR. unfold CRle. intros H. assert (x == x - 0)%CR. ring. rewrite -> H0. assumption. apply CRle_trans with (' proj1_sig c)%CR; auto with *. rewrite -> CRle_Qle; auto with *. 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