proposition: Lemma Metric_d_nneg : forall X : CPsMetricSpace, nneg (Metric_d X).
proof: Proof. intro X. unfold nneg in |- *. intros x y. unfold Metric_d in |- *. simpl in |- *. unfold metric_d in |- *. apply ax_d_nneg. apply CPsMetricSpace_is_CPsMetricSpace. Qed.
imports: CoRN.metrics.Prod_Sub CoRN.metrics.Equiv