Corollary step_async_pt_ext_mapped_simulation_star_1 :
  forall net tr,
    @step_async_star _ multi_fst step_async_init net tr ->
    exists tr', @step_async_star _ multi_snd step_async_init (pt_ext_map_net net) tr'.Definition pt_ext_map_onet (onet : @ordered_network _ multi_fst) : @ordered_network _ multi_snd :=
mkONetwork (fun src dst => filterMap pt_map_msg (onet.(onwPackets) (tot_map_name_inv src) (tot_map_name_inv dst)))
           (fun n => pt_ext_map_data (onet.(onwState) (tot_map_name_inv n)) (tot_map_name_inv n)).

Theorem step_ordered_pt_ext_mapped_simulation_1 : forall net net' tr, @step_ordered _ multi_fst net net' tr -> (exists tr', @step_ordered _ multi_snd (pt_ext_map_onet net) (pt_ext_map_onet net') tr') \/ pt_ext_map_onet net' = pt_ext_map_onet net.