proposition: Lemma CR_epsilon_sign_dec_Gt (e:Qpos) (x:CR) : ((2#1) * proj1_sig e <= approximate x e)%Q -> CR_epsilon_sign_dec e x ≡ Gt.
proof: Proof. intros. unfold CR_epsilon_sign_dec. destruct Q.Qle_dec; intuition. 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