Proof using name_map_bijective.
move => net d h.
apply functional_extensionality => n.
rewrite /update /=.
repeat break_match => //.
- by find_reverse_rewrite; find_rewrite_lem tot_map_name_inverse_inv.
- by find_rewrite; find_rewrite_lem tot_map_name_inv_inverse.
Qed.

Corollary tot_map_update_packet_eq :
forall f p d,
(fun n : name => tot_map_data (update name_eq_dec f (pDst p) d (tot_map_name_inv n))) =
(update name_eq_dec (fun n : name => tot_map_data (f (tot_map_name_inv n))) (pDst (tot_map_packet p)) (tot_map_data d)).