intros; unfold chsubsc_SC in |- *.
elim (fSSC (subjectSC s) u).
intros; unfold fSSC in |- *; apply AddRemEq; auto.
auto.
Qed.

Lemma Close_smCorr :
forall (s : SFSstate) (Sub : SUBJECT) (o : OBJECT),
FuncPre5 s ->
match fsecmat (secmat s) o with
| Some y => set_In Sub (set_union SUBeq_dec (ActReaders y) (ActWriters y))
| None => False
end ->
match fsecmat (close_sm s Sub o) o with
| None => True
| Some y => ~ set_In Sub (ActReaders y) /\ ~ set_In Sub (ActWriters y)
end.