Ltac use_entries_match :=
    match goal with
      | [ _ : eIndex ?e1 = eIndex ?e2,
              H : context [entries_match]
                              |- _ ] =>
        first [ solve [eapply H with (e:=e2)(e':=e1); eauto; congruence] |
                solve [eapply H with (e:=e1)(e':=e2); eauto; congruence]]
    end.Ltac contradict_maxIndex :=
    match goal with
      | [ _ : S (maxIndex ?l) <= eIndex ?e,
              He : In ?e ?l |- _ ] =>
        exfalso; apply maxIndex_is_max in He; intuition; omega
    end.

Lemma logs_sorted_weaken_host : forall net, logs_sorted net -> logs_sorted_host net.