proposition: Lemma Qball_0 : forall a b : Q, Qball 0 a b <-> Qeq a b.
proof: Proof. intros. split. - intros. apply Qle_antisym. + apply (Qplus_le_l _ _ (-b)). rewrite Qplus_opp_r. apply H. + rewrite Qle_minus_iff. apply H. - intros. rewrite H. apply Qball_Reflexive. discriminate. Qed.
imports: CoRN.metric2.Metric CoRN.metric2.Prelength CoRN.metric2.Classification CoRN.model.totalorder.QMinMax CoRN.model.totalorder.QposMinMax Coq.QArith.Qabs CoRN.metric2.UniformContinuity MathClasses.implementations.stdlib_rationals Coq.QArith.Qround