Definition BDDreplace :=
  match BDDvar_make gc cfg ul y with
  | (cfg1, nodey) => BDDsubst cfg1 (nodey :: ul) node x nodey
  end.

Lemma BDDreplace_is_replace : bool_fun_eq (bool_fun_of_BDD (fst BDDreplace) (snd BDDreplace)) (bool_fun_replace x y (bool_fun_of_BDD cfg node)).