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

Lemma extz_sext_eq_rect: forall sz (w: word sz) n1 n2 nsz Hnsz1, exists Hnsz2, eq_rect (n2 + (sz + n1)) word (extz (sext w n1) n2) nsz Hnsz1 = eq_rect (n2 + sz + n1) word (sext (extz w n2) n1) nsz Hnsz2.