Proof using.
intros.
pose proof findAtIndex_in _ _ _ H.
pose proof findAtIndex_index _ _ _ H.
eapply uniqueIndices_elim_eq; eauto.
Qed.
Definition entries_match' entries entries' :=
forall e e' e'',
eIndex e = eIndex e' ->
eTerm e = eTerm e' ->
In e entries ->
In e' entries' ->
eIndex e'' <= eIndex e ->
(In e'' entries -> In e'' entries').

(* Specifications: *)
Lemma entries_match_entries_match' :
forall xs ys,
entries_match xs ys ->
entries_match' xs ys /\
entries_match' ys xs.