intros.
symmetry  in |- *.
rewrite H0 in H.
unfold fsecmat in |- *; apply NotInDOMIsUndef; auto.
Qed.

Lemma NotInDOMIsUndef3 :
forall (s : SFSstate) (p : OBJNAME) (o : OBJECT),
FuncPre1 s ->
FuncPre3 s ->
~ set_In (p, File) (domf (files s)) ->
~ set_In (p, Directory) (domd (directories s)) ->
p = ObjName o -> None = fsecmat (secmat s) o.