Proof using.
move => net failed tr H_st.
have ->: failed = map (@tot_map_name _ _ _ _ orig_multi_params_name_tot_map) failed by rewrite /tot_map_name /= map_id.
have ->: tr = map (@tot_map_trace _ _ _ _ _ orig_multi_params_name_tot_map) tr.
rewrite /tot_map_trace /= /id /= {H_st}.
elim: tr => //=.
by case => a; case => [i|o] l IH; rewrite -IH.
exact: step_ordered_failure_tot_mapped_simulation_star_1.
Qed.

Lemma step_ordered_dynamic_failure_serialize_simulation :
forall net net' failed failed' tr,
NoDup (odnwNodes net) ->
@step_ordered_dynamic_failure _ _ orig_name_overlay_params orig_new_msg_params orig_fail_msg_params (failed, net) (failed', net') tr ->
@step_ordered_dynamic_failure _ _ serialized_name_overlay_params serialized_new_msg_params serialized_fail_msg_params (failed, serialize_odnet net) (failed', serialize_odnet net') tr.