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 pt_msg_in_map : forall m l n m', (forall nm, In nm l -> snd nm = m) -> In (tot_map_name n, m') (filterMap pt_map_name_msg l) -> pt_map_msg m = Some m'.