proposition: Lemma prod_ball_closed : forall e a b, (forall d, 0 < d -> prod_ball (e + d) a b) -> prod_ball e a b.
proof: Proof. intros e a b H. unfold prod_ball in *. split; apply ball_closed; firstorder. Qed.
imports: CoRN.model.totalorder.QposMinMax CoRN.metric2.Metric CoRN.metric2.Classification CoRN.metric2.UniformContinuity CoRN.metric2.Prelength CoRN.metric2.Complete CoRN.metric2.LocatedSubset