Ltac get_invariant_pre inv :=
    match goal with
      | H : raft_intermediate_reachable _ |- _=>
        match (type of H) with
          | context [mkNetwork] =>
            fail 2
        end || copy_apply inv H
    end.Ltac get_invariant_post inv :=
    match goal with
      | H : raft_intermediate_reachable _ |- _=>
        match (type of H) with
          | context [mkNetwork] =>
            copy_apply inv H            
        end
    end.Definition clientCache_to_ks (c : list (clientId * (nat * output))) :=
    map (fun e => (fst e, fst (snd e))) c.

Lemma handleAppendEntries_preserves_lastApplied_entries': forall (p : packet) (net : network) (d : raft_data) (m : msg) (t : term) (n : name) (pli : logIndex) (plt : term) (es : list entry) (ci : logIndex) xs ys ps' st' e, raft_intermediate_reachable net -> raft_intermediate_reachable {| nwPackets := ps'; nwState := st' |} -> (forall h : name, st' h = update name_eq_dec (nwState net) (pDst p) d h) -> (forall p' : packet, In p' ps' -> In p' (xs ++ ys) \/ p' = {| pSrc := pDst p; pDst := pSrc p; pBody := m |}) -> handleAppendEntries (pDst p) (nwState net (pDst p)) t n pli plt es ci = (d, m) -> nwPackets net = xs ++ p :: ys -> pBody p = AppendEntries t n pli plt es ci -> eIndex e <= lastApplied (nwState net (pDst p)) -> In e (log (nwState net (pDst p))) -> In e (log d).