intros sz a b c H.
apply (f_equal (fun x => x ^+ ^~ c)) in H.
repeat rewrite <- wplus_assoc in H.
rewrite wminus_inv in H.
repeat rewrite (wplus_comm _ (wzero sz)) in H.
repeat rewrite wplus_unit in H.
assumption.
Qed.

Lemma lt_word_lt_nat : forall (sz:nat) (n:word sz) (m:nat),
(n < (natToWord sz m))%word ->
(wordToNat n < m)%nat.