induction l as [ | x xs IHxs].
+ intros; simpl in H; inversion H; auto.
+ intros l' l1 l2 Split.
simpl in Split.
destruct l'.
- inversion Split.
- destruct l1.
* destruct (lengthSplit xs l').
+ simpl in *. destruct p. inversion Split.
+ simpl in *. inversion Split.
* simpl in *.
destruct (lengthSplit xs l') eqn:LenSplit.
+ simpl in *. destruct p. inversion Split; subst; clear Split.
pose proof (IHxs l' l1 l2 LenSplit) as Hyp; clear IHxs.
auto.
+ simpl in *. inversion Split.
Qed.

Lemma lengthPathEven : forall p, exists n, length (posToPathAux p) = (2 * n)%nat.
induction p.