Definition inc_in_flight_to_backup (l : list packet) : nat :=
length (filterMap
(fun p => if msg_eq_dec (pBody p) inc
then if name_eq_dec (pDst p) backup
then Some tt else None
else None)
l).

Lemma backup_plus_network_eq_primary :
forall net tr,
step_async_star (params := Counter_MultiParams) step_async_init net tr ->
nwState net backup + inc_in_flight_to_backup (nwPackets net) = nwState net primary.