unfold fOSC in |- *.
intros until z.
cut
match PARTFUNC OBJeq_dec (objectSC s) o with
| Some y => set_In (o, y) (objectSC s)
| None => ~ set_In o (DOM OBJeq_dec (objectSC s))
end.
unfold rmdir_oSC in |- *.
unfold fOSC in |- *.
elim (PARTFUNC OBJeq_dec (objectSC s) o).
intros.
cut (PARTFUNC OBJeq_dec (set_remove OSCeq_dec (o, a) (objectSC s)) o = None).
rewrite H2.
intro.
discriminate H3.
auto.
intros.
discriminate H1.
apply DOMFuncRel4.
Qed.

Lemma EqfOSC7 :
forall (s : SFSstate) (o : OBJECT) (y z : SecClass),
FuncPre6 s ->
fOSC (objectSC s) o = Some y -> fOSC (unlink_oSC s o) o = Some z -> False.