Proof using name_map_bijective multi_map_congr msg_map.
apply functional_extensionality => n.
have H_eq := pt_init_handlers_eq.
rewrite H_eq {H_eq}.
by rewrite tot_map_name_inverse_inv.
Qed.

Lemma filterMap_pt_map_name_msg_empty_eq :
forall l dst,
filterMap pt_map_name_msg l = [] ->
filterMap pt_map_packet (map (fun m0 : name * msg => {| pSrc := dst; pDst := fst m0; pBody := snd m0 |}) l) = [].