Definition forall_ (x : BDDvar) (be : bool_expr) : bool_expr :=
  ANd (restrict x true be) (restrict x false be).Definition be_ex (x : BDDvar) (be : bool_expr) : bool_expr :=
  Or (restrict x true be) (restrict x false be).

(* Specifications: *)
Lemma forall_OK : forall (x : BDDvar) (be : bool_expr), bool_fun_eq (bool_fun_of_bool_expr (forall_ x be)) (bool_fun_forall x (bool_fun_of_bool_expr be)).
Lemma ex_OK : forall (x : BDDvar) (be : bool_expr), bool_fun_eq (bool_fun_of_bool_expr (be_ex x be)) (bool_fun_ex x (bool_fun_of_bool_expr be)).