Definition pt_ext_map_net (net : @network  _ multi_fst) : @network _ multi_snd :=
  {| nwPackets := filterMap pt_map_packet net.(nwPackets) ;
     nwState := fun n => pt_ext_map_data (net.(nwState) (tot_map_name_inv n)) (tot_map_name_inv n) |}.

Theorem step_async_pt_ext_mapped_simulation_1 : forall net net' tr, @step_async _ multi_fst net net' tr -> (exists tr, @step_async _ multi_snd (pt_ext_map_net net) (pt_ext_map_net net') tr) \/ pt_ext_map_net net' = pt_ext_map_net net.