proposition: Lemma inject_Q_AR_plus_nlt : ∀ q r : Q, (ARltS (inject_Q_AR (q + r)) (ARplus (inject_Q_AR q) (inject_Q_AR r)) → False) ∧ (ARltS (ARplus (inject_Q_AR q) (inject_Q_AR r)) (inject_Q_AR (q + r)) → False).
proof: Proof. intros. rewrite <- AReq_nlt. pose proof (inject_Q_AR_plus q r). simpl in H5. simpl. exact H5. Qed.
imports: Coq.Reals.Abstract.ConstructiveReals CoRN.reals.faster.ARArith CoRN.reals.faster.ARabs CoRN.metric2.Metric CoRN.metric2.Complete CoRN.metric2.MetricMorphisms CoRN.model.metric2.Qmetric CoRN.model.totalorder.QposMinMax CoRN.reals.fast.CRArith CoRN.reals.fast.CRabs ConstructiveFastReals