Definition BDDex :=
  match BDDneg gc cfg ul node with
  | (cfg1, node1) =>
      match BDDuniv cfg1 (node1 :: ul) y node1 with
      | (cfg2, node2) => BDDneg gc cfg2 (node2 :: ul) node2
      end
  end.

Lemma BDDex_used_nodes_preserved : used_nodes_preserved cfg (fst BDDex) ul.