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_neq_lemma : forall bf1 bf2 : bool_fun, ~ bool_fun_eq bf1 bf2 -> ~ bool_fun_eq bf2 bf1.