In raft paper section 5.4.2
If a leader crashes before committing an entry, future leaders will attempt to finish replicating the entry. However, a le
After S1 replicates entry 4 with a higher term than 2 and 3. S5 will no longer be elected as leader, since the leader election strategy of Raft:
Raft determines which of two logs is more up-to-date by comparing the index and term of the last entries in the logs. If the logs have last entries with different terms, then the log with the later term is more up-to-date. If the logs end with the same term, then whichever log is longer is more up-to-date.
So, in my opinion, the appended log entry 4 in (e) implicitly promote all the entries' term before it. Because what we only care about is the term or the last entry, rather than entry 2 any more.
This is just like what the proposer do in Phase 2 of Paxos:
If the proposer receives a response to its prepare requests (numbered n) from a majority of acceptors, then it sends an accept request to each of those acceptors for a proposal numbered n with a value v, where v is the value of the highest-numbered proposal among the responses, or is any value if the responses reported no proposals.
That's say, propose the learned value 2 with a higher propose number.