induction ls1; intuition.
inversion H; clear H; subst.
rewrite <- app_comm_cons.
econstructor.
intuition.
eapply in_app_or in H.
intuition.
eapply H1.
simpl.
left.
eauto.
trivial.
eapply IHls1; eauto.
intuition.
eapply H1.
simpl.
right.
eauto.
eauto.
intuition.
eapply H1.
simpl.
right.
eauto.
eauto.
Qed.

Lemma allNatsLt_NoDup :
forall (n : nat),
NoDup (allNatsLt n).