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

Lemma wtl_nat_cast_WS: forall n m (q: n = m) (p: S n = S m) (w: word n) (b: bool), wtl (nat_cast word p (WS b w)) = nat_cast word q w.