Definition bool_fun_if (x : BDDvar) (bf bf' : bool_fun) : bool_fun :=
  fun vb : var_binding => ifb (vb x) (bf vb) (bf' vb).

Lemma bool_fun_if_lemma_2 : forall (cfg : BDDconfig) (node : ad), BDDconfig_OK cfg -> is_internal_node cfg node -> bool_fun_eq (bool_fun_of_BDD cfg node) (bool_fun_if (var cfg node) (bool_fun_of_BDD cfg (high cfg node)) (bool_fun_of_BDD cfg (low cfg node))).