intros; unfold chobjsc_SC in |- *.
cut
match fOSC (objectSC s) o with
| Some y => set_In (o, y) (objectSC s)
| None => ~ set_In o (DOM OBJeq_dec (objectSC s))
end.
split.
intro H1; rewrite H1; auto.
generalize H0; elim (fOSC (objectSC s) o).
intro; intro;
replace
(fOSC
(set_add OSCeq_dec (o, sc) (set_remove OSCeq_dec (o, a) (objectSC s))) o)
with (Some sc).
intro H2; discriminate H2.
unfold fOSC in |- *; apply AddEq1.
auto.
auto.
unfold fOSC in |- *; apply DOMFuncRel4.
Qed.

Lemma Aux1 :
forall y : SecClass, ~ (Some y = None <-> None = None :>option SecClass).