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.