Ltac wlt_ind :=
  match goal with
  | [ |- forall (n: word ?len), ?P ] =>
    refine (well_founded_ind (@wlt_wf len) (fun n => P) _)
  end.

Lemma wlshift_sext_extz: forall sz (w: word sz) n, existT word _ (wlshift (sext w n) n) = existT word _ (extz w n).