intros.
cut (~ set_In u (ActReaders rw) /\ ~ set_In u (ActWriters rw)).
tauto.
auto.
Qed.

Lemma UniqNames :
forall (s : SFSstate) (o : OBJECT),
FuncPre1 s ->
~ set_In (ObjName o, File) (domf (files s)) ->
~ set_In (ObjName o, Directory) (domd (directories s)) ->
~ set_In o (DOM OBJeq_dec (acl s)).