(* 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).

Theorem handleAppendEntriesReply_log_term_type : forall h st n t es r st' ps, handleAppendEntriesReply h st n t es r = (st', ps) -> (log st' = log st /\ currentTerm st' = currentTerm st /\ type st' = type st) \/ type st' = Follower.