Proof using rri.
unfold candidateEntriesTerm_lowered,
cronies_correct, votes_correct.
intros. break_and.
rewrite deghost_spec.
find_apply_lem_hyp deghost_packet_exists.
find_apply_lem_hyp deghost_packet_exists.
break_exists.  break_and. subst.
eapply_prop_hyp votes_nw pBody. concludes.
eapply_prop_hyp prevLog_candidateEntriesTerm pBody; auto.
concludes.
unfold candidateEntriesTerm in *. break_exists. break_and.
match goal with
| H : wonElection _ = _ |- _ =>
eapply wonElection_one_in_common in H; [|clear H; eauto]
end.
break_exists. break_and.
repeat match goal with
| [ H : _ |- _ ] => rewrite deghost_spec in H
end.
simpl in *.
break_or_hyp.
- apply_prop_hyp cronies_votes In.
assert (pDst x = x1) by (eapply_prop one_vote_per_term; eauto).
subst. auto.
- intro.
assert (pDst x = x1).
{ eapply_prop one_vote_per_term;
eapply_prop cronies_votes.
- eapply_prop votes_received_cronies; eauto.
- repeat find_reverse_rewrite. auto.
}
subst.
concludes. contradiction.
Qed.

(* Specifications: *)
Lemma prevLog_candidateEntriesTerm_lowered :
forall net,
raft_intermediate_reachable net ->
forall p p' t leaderId prevLogIndex prevLogTerm entries leaderCommit,
In p (nwPackets net) ->
pBody p = AppendEntries t leaderId prevLogIndex prevLogTerm
entries leaderCommit ->
0 < prevLogTerm ->
candidateEntriesTerm_lowered net prevLogTerm p'.