Proof using.
induction l; intros; intro.
- intuition.
- simpl in *. break_match; try discriminate. intuition.
+ subst. rewrite <- beq_nat_refl in *. discriminate.
+ find_copy_apply_hyp_hyp. intuition. break_if; do_bool; eauto. omega.
Qed.

Lemma findAtIndex_in :
forall l i e',
findAtIndex l i = Some e' ->
In e' l.