unfold DACSecureState in |- *.
intros.
cut
match fsecmat (secmat s) o with
| Some y =>
(set_In u (ActReaders y) -> PreDACRead s u o) /\
(set_In u (ActWriters y) -> PreDACWrite s u o)
| None => True
end.
elim (fsecmat (secmat s) o).
intros.
elim H0; intros.
auto.
auto.
apply H.
Qed.

Lemma ReadWriteImpWrite :
forall s : SFSstate,
DACSecureState s ->
forall (u : SUBJECT) (o : OBJECT),
match fsecmat (secmat s) o with
| Some y => set_In u (ActWriters y) -> PreDACWrite s u o
| None => True
end.