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

Lemma else_0_to_ex_N: forall (b: bool) (a: N), exists k, (if b then a else 0%N) = (k * a)%N.