Definition BDDiff :=
  match BDDor cfg ul node1 node2 with
  | (cfg1, node3) =>
      match BDDand cfg1 (node3 :: ul) node1 node2 with
      | (cfg2, node4) => BDDimpl cfg2 (node4 :: node3 :: ul) node3 node4
      end
  end.

Lemma BDDiff_list_OK_cons : used_list_OK (fst BDDiff) (snd BDDiff :: ul).