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

Theorem eq_rect_split2_eq2 : forall n1 n2 n2' (w : word (n1 + n2)) Heq Heq2, eq_rect n2 (fun n => word n) (split2 n1 n2 w) n2' Heq = split2 n1 n2' (eq_rect (n1+n2) (fun n => word n) w (n1+n2') Heq2).