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 wordToNat_natToWord_pred:
forall {sz} (w: word sz), w <> wzero sz ->
pred (wordToNat w) =
wordToNat (w ^- (natToWord sz 1)).