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

Lemma WS_eq_rect : forall b n (w: word n) n' H H', eq_rect _ word (@WS b n w) _ H = @WS b n' (eq_rect _ word w _ H').