(*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 NotInDOMIsUndef3 : forall (s : SFSstate) (p : OBJNAME) (o : OBJECT), FuncPre1 s -> FuncPre3 s -> ~ set_In (p, File) (domf (files s)) -> ~ set_In (p, Directory) (domd (directories s)) -> p = ObjName o -> None = fsecmat (secmat s) o.