(*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_smCorr2 : forall (s : SFSstate) (Sub u0 : 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, fsecmat (secmat s) o with | _, None => False | None, Some z => True | Some y, Some z => (set_In u0 (ActReaders y) -> set_In u0 (ActReaders z)) /\ (set_In u0 (ActWriters y) -> set_In u0 (ActWriters z)) end.