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_independent_zero : forall (cfg : BDDconfig) (x : BDDvar), BDDconfig_OK cfg -> bool_fun_independent (bool_fun_of_BDD cfg BDDzero) x.