Proof using.
move => net.
rewrite /deserialize_net.
rewrite /pt_map_net /pt_map_data /= /id /= /pt_map_packet.
set fm := filterMap _ _.
set fm' := filterMap _ _.
suff H_eq: fm = fm' by rewrite H_eq.
rewrite /fm /fm'.
clear.
rewrite /pt_map_packet /tot_map_name /= /deserialize_packet.
elim (nwPackets net) => //=.
case => [src dst body] /= l IH.
rewrite IH.
by case (deserialize_top deserialize _).
Qed.

(* Specifications: *)
Lemma pt_map_onet_deserialize_onet :
forall net, pt_map_onet net = deserialize_onet net.