Proof using.
unfold contiguous_range_exact_lo.
intuition.
Qed.

Lemma lifted_sms_nw :
forall (net : network (params := raft_refined_multi_params)) h p t leaderId prevLogIndex prevLogTerm entries leaderCommit e,
state_machine_safety (deghost net) ->
In p (nwPackets net) ->
pBody p = AppendEntries t leaderId prevLogIndex prevLogTerm
entries leaderCommit ->
t >= currentTerm (snd (nwState net h)) ->
commit_recorded (deghost net) h e ->
(prevLogIndex > eIndex e \/
(prevLogIndex = eIndex e /\ prevLogTerm = eTerm e) \/
eIndex e > maxIndex entries \/
In e entries).