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 BDDvar_independent_1 : forall (cfg : BDDconfig) (n : nat) (node : ad) (x : BDDvar), BDDconfig_OK cfg -> is_internal_node cfg node -> n = nat_of_N (var cfg node) -> BDDcompare (var cfg node) x = Datatypes.Lt -> bool_fun_independent (bool_fun_of_BDD cfg node) x.