Definition nextIndex_preserved st st' :=
    (type st' = Leader ->
     type st = Leader /\
     maxIndex (log st) <= maxIndex (log st') /\
     nextIndex st' = nextIndex st).

Lemma handleAppendEntries_nextIndex_preserved : forall h st t n pli plt es ci st' ps, handleAppendEntries h st t n pli plt es ci = (st', ps) -> nextIndex_preserved st st'.