elim (classic (closure X f)).
intro clXf.
elim (clXf n).
simple induction 1.
intros; exists x.
split; trivial.
unfold union in |- *.
left; trivial.
intro notclXf.
exists f; intros.
split; trivial.
unfold union in |- *.
right; trivial.
Qed.
Hint Resolve density.

(* Specifications: *)
Theorem Rem :
forall X : Top,
exists Y : Top, (exists Z : Top, closed Y /\ dense Z /\ equal X (inter Y Z)).