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.