Definition bool_fun_independent (bf : bool_fun) (x : BDDvar) :=
forall vb : var_binding,
bool_fun_eval bf (augment vb x true) =
bool_fun_eval bf (augment vb x false).

Lemma bool_fun_of_BDDlow :
forall (cfg : BDDconfig) (node : ad),
BDDconfig_OK cfg ->
is_internal_node cfg node ->
bool_fun_eq (bool_fun_of_BDD cfg (low cfg node))
(bool_fun_restrict (bool_fun_of_BDD cfg node) (var cfg node) false).