proposition: Lemma FinSubset_ball_triangle_l : forall e1 e2 x1 x2 l, (ball e1 x1 x2) -> FinSubset_ball e2 x2 l -> FinSubset_ball (e1 + e2) x1 l.
proof: Proof. intros. intro abs. unfold FinSubset_ball in H0. contradict H0; intros [y H0]. contradict abs. exists y. split. apply H0. eapply ball_triangle. apply H. apply H0. Qed.
imports: CoRN.model.totalorder.QposMinMax CoRN.metric2.Hausdorff CoRN.logic.Classic CoRN.stdlib_omissions.List CoRN.metric2.Classification CoRN.metric2.Complete CoRN.metric2.Prelength