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

Theorem eq_rect_split1_eq2 : forall n1 n2 n2' (w: word (n1 + n2)) Heq, split1 n1 n2 w = split1 n1 n2' (eq_rect (n1 + n2) (fun y : nat => word y) w (n1 + n2') Heq).