Ltac shatterer := simpl; intuition;
  match goal with
    | [ w : _ |- _ ] => rewrite (shatter_word w); simpl
  end; f_equal; auto.

Lemma wtl_eq_rect : forall n w Heq Heq', wtl (eq_rect (S n) word w (S (n + 0)) Heq) = eq_rect n word (wtl w) (n + 0) Heq'.