Proof using.
unfold deghost.
simpl.
intros.
do_in_map.
eauto.
Qed.

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'.