Definition terms_and_indices_from_one_log_ind (net : network) : Prop :=
    terms_and_indices_from_one_log net /\ terms_and_indices_from_one_log_nw net.

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.