Definition BDDimpl :=
  match BDDneg cfg ul node1 with
  | (cfg1, node1') => BDDor cfg1 (node1' :: ul) node1' node2
  end.

Lemma BDDimpl_is_impl : bool_fun_eq (bool_fun_of_BDD (fst BDDimpl) (snd BDDimpl)) (bool_fun_impl (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2)).