trivial. Qed.

(* Specifications: *)
Lemma uhwm_eq : forall x y : Z_ (2 ^ w), _Z (uhwm x y) = (x * y) / 2 ^ w.
trivial. Qed.
Lemma ltw_true : forall x y t e : Z_ (2 ^ w), x < y -> ltw x y t e = t.
unfold ltw. unfold Zlt_bool. unfold Zlt. intros x y t e H. rewrite H.
Lemma ltw_false : forall x y t e : Z_ (2 ^ w), y <= x -> ltw x y t e = e.
intros x y t e H. unfold ltw. unfold Zlt_bool. cut (x >= y). unfold Zge.