unfold equal, inclusion in |- *; intro X; split.
unfold inter, union, closure in |- *; intros.
split.
intro n; exists z; split; auto.
left; trivial.
unfold inter, union, closure in |- *; intros.
elim H; intros.
elim H1; trivial.
unfold complement in |- *; intros.
elim (H2 H0).
Qed.

(* Specifications: *)
Lemma density : forall X : Top, dense (union X (complement (closure X))).
unfold dense in |- *; intros X f n.