Lemma no_entries_past_current_term_unaffected : forall net st' ps' xs p ys d ms, nwPackets net = xs ++ p :: ys -> no_entries_past_current_term net -> (forall h : Net.name, st' h = update name_eq_dec (nwState net) (pDst p) d h) -> (forall p' : packet, In p' ps' -> In p' (xs ++ ys) \/ In p' (send_packets (pDst p) ms)) -> currentTerm (nwState net (pDst p)) <= currentTerm d -> log d = log (nwState net (pDst p)) -> (forall m, In m ms -> ~ is_append_entries (snd m)) -> no_entries_past_current_term {| nwPackets := ps'; nwState := st' |}.