Corollary wmsb_Zabs_pos:
  forall sz (w: word sz),
    wmsb w false = false -> Z.abs (wordToZ w) = wordToZ w.Corollary wmsb_Zabs_neg:
  forall sz (w: word sz),
    wmsb w false = true -> (Z.abs (wordToZ w) = - wordToZ w)%Z.

Lemma word_exists_bound: forall sz z, (- Z.of_nat (pow2 sz) <= z < Z.of_nat (pow2 sz))%Z -> exists w: word (S sz), wordToZ w = z.