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 BDDunique : forall cfg : BDDconfig, BDDconfig_OK cfg -> forall node1 node2 : ad, config_node_OK cfg node1 -> config_node_OK cfg node2 -> bool_fun_eq (bool_fun_of_BDD cfg node1) (bool_fun_of_BDD cfg node2) -> node1 = node2.