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 split1_split2 : forall n1 n2 n3 Heq w,
split1 n2 n3 (split2 n1 (n2 + n3) w) =
split2 n1 n2 (split1 (n1 + n2) n3 (match Heq in _ = N return word N with
| refl_equal => w
end)).