intros until o; unfold ownerclose_sm in |- *.
intro.
generalize H.
elim (fsecmat (secmat s) o).
intros y H0; discriminate H0.
auto.
Qed.

Lemma Open_smCorr3 :
forall (s : SFSstate) (Sub : SUBJECT) (o : OBJECT) (m : MODE),
FuncPre5 s ->
fsecmat (open_sm s Sub o m) o = None -> fsecmat (secmat s) o = None.