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

Lemma nat_cast_inj: forall sz sz' (p: sz = sz') (w1 w2: word sz), nat_cast word p w1 = nat_cast word p w2 -> w1 = w2.