Definition candidateEntriesTerm_lowered (net : network) t p : Prop :=
    In p (nwPackets net) ->
    pBody p = RequestVoteReply t true ->
    currentTerm (nwState net (pDst p)) = t ->
    wonElection (dedup name_eq_dec (pSrc p :: votesReceived (nwState net (pDst p)))) = true ->
    type (nwState net (pDst p)) <> Candidate.

Lemma prevLog_candidateEntriesTerm_lowered' : forall net, prevLog_candidateEntriesTerm net -> votes_correct net -> cronies_correct net -> forall p p' t leaderId prevLogIndex prevLogTerm entries leaderCommit, In p (nwPackets (deghost net)) -> pBody p = AppendEntries t leaderId prevLogIndex prevLogTerm entries leaderCommit -> 0 < prevLogTerm -> candidateEntriesTerm_lowered (deghost net) prevLogTerm p'.