StartPSP.
inversion H.
unfold StarProperty in |- *; simpl in |- *; intros.
elim (OBJeq_dec o o1); elim (OBJeq_dec o o2); intros EQ2 EQ1.
replace (fsecmat (secmat s) o1) with (None (A:=ReadersWriters)).
elim (fOSC (objectSC s) o2); elim (fOSC (objectSC s) o1);
elim (fOSC (rmdir_oSC s o) o2); elim (fOSC (rmdir_oSC s o) o1);
elim (fsecmat (secmat s) o2); trivial.
rewrite <- EQ1; symmetry  in |- *; unfold fsecmat in |- *; auto.
replace (fsecmat (secmat s) o1) with (None (A:=ReadersWriters)).
elim (fsecmat (secmat s) o2); elim (fOSC (objectSC s) o2);
elim (fOSC (objectSC s) o1); elim (fOSC (rmdir_oSC s o) o2);
elim (fOSC (rmdir_oSC s o) o1); trivial.
rewrite <- EQ1; symmetry  in |- *; unfold fsecmat in |- *; auto.
replace (fsecmat (secmat s) o2) with (None (A:=ReadersWriters)).
elim (fsecmat (secmat s) o1); elim (fOSC (objectSC s) o2);
elim (fOSC (objectSC s) o1); elim (fOSC (rmdir_oSC s o) o2);
elim (fOSC (rmdir_oSC s o) o1); trivial.
rewrite <- EQ2; symmetry  in |- *; unfold fsecmat in |- *; auto.
replace (fOSC (rmdir_oSC s o) o2) with (fOSC (objectSC s) o2).
replace (fOSC (rmdir_oSC s o) o1) with (fOSC (objectSC s) o1).
unfold StarProperty in SP; apply SP.
auto.
auto.
Qed.

Lemma RmdirPCP :
forall s t : SFSstate,
FuncPre4 s -> FuncPre6 s -> PreservesControlProp s Rmdir t.