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

Lemma combine_sext: forall sz1 (w1: word sz1) sz2 (w2: word (S sz2)) n, existT word _ (combine w1 (sext w2 n)) = existT word _ (sext (combine w1 w2) n).