intros; unfold fOSC, chobjsc_SC in |- *.
elim (fOSC (objectSC s) o1).
intro; apply AddRemEq; auto.
auto.
Qed.

Lemma EqfOSC5 :
forall (s : SFSstate) (o : OBJECT) (p : OBJNAME),
FuncPre1 s ->
FuncPre2 s ->
~ set_In (p, File) (domf (files s)) ->
~ set_In (p, Directory) (domd (directories s)) ->
p = ObjName o -> None = fOSC (objectSC s) o.