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 zext_size: forall sz n (w: word (sz + n)), (- Z.of_nat (pow2 sz) <= wordToZ w < Z.of_nat (pow2 sz))%Z -> wmsb w false = false -> exists sw, w = zext sw n.