induction n1 as [|n1 IHn1]; simpl; intros n2 n3 Heq w; intuition.
rewrite (UIP_dec eq_nat_dec Heq (refl_equal _)); reflexivity.
rewrite (IHn1 _ _ (plus_assoc _ _ _)).
f_equal.
apply wtl_match.
Qed.

Theorem split2_split1 : forall n1 n2 n3 Heq w,
split2 n1 n2 (split1 (n1+n2) n3 w) =
split1 n2 n3 (split2 n1 (n2+n3) (match Heq in _ = N return word N with
| refl_equal => w
end)).