unfold close_sm, fsecmat in |- *; intros;
elim (PARTFUNC OBJeq_dec (secmat s) o1).
intro; elim (set_remove SUBeq_dec u (ActReaders a));
elim (set_remove SUBeq_dec u (ActWriters a)).
auto.
auto.
auto.
auto.
auto.
Qed.

(* Specifications: *)
Lemma Close_smCorr3 :
forall (s : SFSstate) (Sub : SUBJECT) (o : OBJECT),
fsecmat (secmat s) o = None -> fsecmat (close_sm s Sub o) o = None.