Proof using name_map_bijective.
move => ns f h m from to ms.
rewrite -map_msg_update2.
by rewrite collate_ls_tot_map_eq.
Qed.

(* Specifications: *)
Theorem step_ordered_dynamic_failure_tot_mapped_simulation_1 :
forall net net' failed failed' tr,
NoDup (odnwNodes net) ->
@step_ordered_dynamic_failure _ _ overlay_fst new_msg_fst fail_msg_fst (failed, net) (failed', net') tr ->
@step_ordered_dynamic_failure _ _ overlay_snd new_msg_snd fail_msg_snd (map tot_map_name failed, tot_map_odnet net) (map tot_map_name failed', tot_map_odnet net') (map tot_map_trace tr).