Corollary step_ordered_pt_mapped_simulation_star_1 :
  forall net tr,
    @step_ordered_star _ multi_fst step_ordered_init net tr ->
    @step_ordered_star _ multi_snd step_ordered_init (pt_map_onet net) (filterMap pt_map_trace_ev tr).

Lemma nodup_pt_map : forall m nms, (forall nm, In nm nms -> snd nm = m) -> NoDup nms -> NoDup (filterMap pt_map_name_msg nms).