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

(* Specifications: *)
Lemma TwoImpRight :
forall (s : SFSstate) (u : SUBJECT),
(forall rw : ReadersWriters,
set_In rw (ransecmat (secmat s)) ->
~ set_In u (ActReaders rw) /\ ~ set_In u (ActWriters rw)) ->
forall rw : ReadersWriters,
set_In rw (ransecmat (secmat s)) -> ~ set_In u (ActWriters rw).
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)).