Definition lifted_no_entries_past_current_term_host net :=
    forall (h : name) e,
      In e (log (snd (nwState net h))) ->
      eTerm e <= currentTerm (snd (nwState net h)).

Lemma handleAppendEntries_lastApplied : forall h st t n pli plt es ci st' m, handleAppendEntries h st t n pli plt es ci = (st', m) -> lastApplied st' = lastApplied st.