(* matchIndex *)
  Definition matchIndex_preserved st st' :=
    type st' = Leader ->
    (type st = Leader /\ matchIndex st' = matchIndex st /\ log st' = log st).Definition matchIndex_preserved_except_at_host h st st' :=
    type st' = Leader ->
    (type st = Leader /\
     forall h',
       h <> h' ->
       (assoc_default name_eq_dec (matchIndex st') h' 0) = (assoc_default name_eq_dec (matchIndex st) h') 0).

Lemma doLeader_message_entries : forall st h os st' ms m t n pli plt es ci e, doLeader st h = (os, st', ms) -> In m ms -> snd m = AppendEntries t n pli plt es ci -> In e es -> In e (log st).