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 no_duplicate_node : forall (cfg : BDDconfig) (node1 node2 : ad), BDDconfig_OK cfg -> is_internal_node cfg node1 -> is_internal_node cfg node2 -> var cfg node1 = var cfg node2 -> high cfg node1 = high cfg node2 -> low cfg node1 = low cfg node2 -> node1 = node2.