rewrite Z.add_0_r. rewrite <- Int.unsigned_repr_eq.
rewrite Int.repr_unsigned.
apply Int.repr_unsigned.
Qed.

(* Specifications: *)
Lemma sum_sym a b: sum a b = sum b a.
unfold sum. rewrite Z.add_comm. trivial. Qed.
Lemma sum_zero_l a: sum Int.zero a = a.
rewrite sum_sym. apply sum_zero_r. Qed.