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))).