Proof using.
elim => //=.
case => /= n m l IH dst.
rewrite /pt_map_name_msg /=.
case pt_map_msg => [m'|] H_eq //=.
by rewrite IH.
Qed.

Lemma filterMap_pt_map_packet_map_eq :
forall l h,
filterMap pt_map_packet (map (fun m : name * msg => {| pSrc := h; pDst := fst m; pBody := snd m |}) l) =
map (fun m : name * msg => {| pSrc := tot_map_name h; pDst := fst m; pBody := snd m |}) (filterMap pt_map_name_msg l).