(*SUBJECT, Property and TransFunc*)
Ltac OpDontChangeStPSS :=
intros s t Sub SS TF; inversion TF;
match goal with
| id:(s = t) |- _ => rewrite <- id; auto
end.
Ltac OpDontChangeStPSP :=
intros s t Sub SP TF;  (* SUBJECT, Property and TransFunc *)
inversion TF; match goal with
| id:(s = t) |- _ => rewrite <- id; auto
end.
Ltac StartPSS := intros s t Sub SS TF; inversion TF.
Ltac BreakSS :=
match goal with
| SS:(SecureState _) |- _ =>
unfold SecureState in SS; elim SS; intros DAC MAC
end.
Ltac StartPSP := intros s t Sub SP TF; inversion TF.

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