induction ls; intuition; simpl in *.
econstructor.
remember (split ls) as z.
destruct z.
destruct a.
simpl in *.
inversion H; clear H; subst.
econstructor.
intuition.
eapply in_split_r in H.
rewrite <- Heqz in H.
simpl in *.
intuition.
intuition.
Qed.
Fixpoint forNats(n : nat) :=
match n with
| 0 => nil
| S n' =>
cons n' (forNats n')
end.

(* Specifications: *)
Lemma forNats_In :
forall n i,
i < n <->
In i (forNats n).