Proof using.
split.
- unfold terms_and_indices_from_one_log, terms_and_indices_from_one. simpl. contradiction.
- unfold terms_and_indices_from_one_log_nw, terms_and_indices_from_one. simpl. contradiction.
Qed.

Lemma taifol_no_append_entries :
forall ps' net ms p t leaderId prevLogIndex prevLogTerm entries leaderCommit h,
(forall (p : packet), In p ps' -> In p (nwPackets net) \/ In p (send_packets h ms)) ->
(forall m, In m ms -> ~ is_append_entries (snd m)) ->
In p ps' ->
pBody p = AppendEntries t leaderId prevLogIndex prevLogTerm entries leaderCommit ->
terms_and_indices_from_one_log_nw net ->
terms_and_indices_from_one entries.