Proof using.
induction xs; intros; simpl in *; intuition; break_match; try discriminate.
- subst. do_bool. congruence.
- do_bool. break_if; eauto.
do_bool. find_apply_hyp_hyp. intuition.
Qed.

(* Specifications: *)
Lemma findAtIndex_removeAfterIndex_agree :
forall xs i j e e',
NoDup (map eIndex xs) ->
findAtIndex xs i = Some e ->
findAtIndex (removeAfterIndex xs j) i = Some e' ->
e = e'.