Definition lifted_in_log_in_all_entries (net : network) :=
    forall h e,
      In e (log (snd (nwState net h))) ->
      exists t,
        In (t, e) (allEntries (fst (nwState net h))).

Lemma update_elections_data_appendEntries_preserves_allEntries' : forall st h t n pli plt es ci x, In x (allEntries (fst st)) -> In x (allEntries (update_elections_data_appendEntries h st t n pli plt es ci)).