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).

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)).