Definition pt_map_onet_event e :=
{| evt_a := (List.map tot_map_name (fst e.(evt_a)), pt_map_onet (snd e.(evt_a))) ;
   evt_l := tot_map_label e.(evt_l) ;
   evt_trace := filterMap pt_map_trace_ev e.(evt_trace) |}.

Lemma pt_map_onet_tot_map_label_event_state_weak_fairness : forall s, lb_step_execution lb_step_ordered_failure s -> weak_fairness lb_step_ordered_failure label_silent s -> weak_fairness lb_step_ordered_failure label_silent (map pt_map_onet_event s).