Section rmdirIsSecure.
StartPSS.
inversion H.
unfold SecureState in |- *; BreakSS; split.
unfold DACSecureState in |- *; simpl in |- *; intros.
elim (OBJeq_dec o o0); intros.
rewrite <- a.
replace (fsecmat (secmat s) o) with (None (A:=ReadersWriters)).
trivial.
symmetry  in |- *; unfold fsecmat in |- *; auto.
unfold PreDACRead, PreDACWrite in |- *; simpl in |- *.
replace (facl (rmdir_acl s o) o0) with (facl (acl s) o0).
unfold DACSecureState, PreDACRead, PreDACWrite in DAC; apply DAC.
auto.
unfold MACSecureState in |- *; simpl in |- *.
intros.
elim (OBJeq_dec o o0).
intro; rewrite <- a.
replace (fsecmat (secmat s) o) with (None (A:=ReadersWriters)).
elim (fOSC (rmdir_oSC s o) o); elim (fSSC (subjectSC s) u0); trivial.
symmetry  in |- *; unfold fsecmat in |- *; auto.
intro EQ.
replace (fOSC (rmdir_oSC s o) o0) with (fOSC (objectSC s) o0).
unfold MACSecureState in MAC; apply MAC.
auto.
Qed.

Lemma RmdirPSP :
forall (s t : SFSstate) (u : SUBJECT),
StarProperty s -> TransFunc u s Rmdir t -> StarProperty t.