Definition bool_fun_of_BDD (cfg : BDDconfig) (node : ad) :=
bool_fun_of_BDD_1 cfg node (S (nat_of_N (var cfg node))).

Lemma bool_fun_of_BDD_semantics :
forall cfg : BDDconfig,
BDDconfig_OK cfg ->
bool_fun_of_BDD cfg BDDzero = bool_fun_zero /\
bool_fun_of_BDD cfg BDDone = bool_fun_one /\
(forall node : ad,
is_internal_node cfg node ->
bool_fun_of_BDD cfg node =
(fun vb : var_binding =>
if vb (var cfg node)
then bool_fun_of_BDD cfg (high cfg node) vb
else bool_fun_of_BDD cfg (low cfg node) vb)).