Proof using.
move => net.
rewrite /tot_map_odnet.
rewrite /tot_map_name /= /id /= map_id.
rewrite /serialize_odnet.
set f := fun _ => match _ with _ => _ end.
by have ->: odnwState net = f by rewrite /f; apply functional_extensionality => n; case: odnwState.
Qed.

Lemma step_async_serialize_simulation :
forall net net' tr,
@step_async _ orig_multi_params net net' tr ->
@step_async _ serialized_multi_params (serialize_net net) (serialize_net net') tr.