(* 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 handleClientRequest_matchIndex_maxIndex: forall h st client id c out st' ps, handleClientRequest h st client id c = (out, st', ps) -> (maxIndex (log st') = maxIndex (log st) /\ matchIndex st' = matchIndex st) \/ (assoc_default name_eq_dec (matchIndex st') h 0) = maxIndex (log st').