intros until o; elim o; simpl in |- *.
intros until b; elim b; intros.
rewrite <- H3.
symmetry  in |- *; unfold fsecmat in |- *; apply NotInDOMIsUndef.
cut (~ set_In (p, File) (DOM OBJeq_dec (acl s))).
unfold FuncPre3, Included in H3.
unfold FuncPre3, Included in H0.
auto.
apply UniqNames; auto.
rewrite <- H3.
symmetry  in |- *; unfold fsecmat in |- *; apply NotInDOMIsUndef.
cut (~ set_In (p, Directory) (DOM OBJeq_dec (acl s))).
unfold FuncPre3, Included in H3.
unfold FuncPre3, Included in H0.
auto.
apply UniqNames; auto.
Qed.

Lemma EqfOSC6 :
forall (s : SFSstate) (o1 o2 : OBJECT) (sc : SecClass),
o1 <> o2 -> fOSC (objectSC s) o2 = fOSC (chobjsc_SC s o1 sc) o2.