Fixpoint int_of_one_bits (l: list int) : int :=
  match l with
  | nil => zero
  | a :: b => add (shl one a) (int_of_one_bits b)
  end.

Lemma translate_ltu: forall x y d, 0 <= unsigned x + unsigned d <= max_unsigned -> 0 <= unsigned y + unsigned d <= max_unsigned -> ltu (add x d) (add y d) = ltu x y.