Definition sequence_equality (net : seq_num_network) :=
    forall p p',
      In p (nwPackets net) ->
      In p' (nwPackets net) ->
      (tmNum (pBody p)) = (tmNum (pBody p')) ->
      pSrc p = pSrc p' ->
      p = p'.

Lemma processPackets_dedup : forall processed (rest : list seq_num_packet) n' l h net, (forall p, In p rest -> In p (nwPackets net)) -> sequence_sane net -> processPackets (tdNum (nwState net h)) l = (n', processed) -> dedup pkt_eq_dec ((@send_packets _ multi_params h processed) ++ rest) = (send_packets h processed) ++ (dedup pkt_eq_dec rest).