Proof using name_map_bijective.
move => f.
case => src dst m d.
exact: tot_map_update_eq.
Qed.

Lemma tot_map_packet_map_eq :
forall l h,
map tot_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 |}) (tot_map_name_msgs l).