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 internal_node_not_constant_1 :
forall cfg : BDDconfig,
BDDconfig_OK cfg ->
forall (n : nat) (node : ad),
is_internal_node cfg node ->
n = nat_of_N (var cfg node) ->
~ bool_fun_eq (bool_fun_of_BDD cfg node) bool_fun_zero /\
~ bool_fun_eq (bool_fun_of_BDD cfg node) bool_fun_one.