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

Theorem combine_split_eq_rect2 : forall n1 n2 n2' (w : word (n1 + n2)) Heq, combine (split1 n1 n2 w) (eq_rect n2 (fun n => word n) (split2 n1 n2 w) n2' Heq) = eq_rect (n1 + n2) (fun n => word n) w (n1 + n2') (eq_rect_split2_helper _ Heq).