proposition: Lemma FinSubset_ball_weak_le : forall (e1 e2:Q) x l, e1 <= e2 -> FinSubset_ball e1 x l -> FinSubset_ball e2 x l.
proof: Proof. intros. intro abs. unfold FinSubset_ball in H0. contradict H0; intros [y [iny H0]]. contradict abs. exists y. split. exact iny. apply (ball_weak_le X x y H), 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