(*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 Close_smCorr : forall (s : SFSstate) (Sub : SUBJECT) (o : OBJECT), FuncPre5 s -> match fsecmat (secmat s) o with | Some y => set_In Sub (set_union SUBeq_dec (ActReaders y) (ActWriters y)) | None => False end -> match fsecmat (close_sm s Sub o) o with | None => True | Some y => ~ set_In Sub (ActReaders y) /\ ~ set_In Sub (ActWriters y) end.