Definition tot_map_net_event e :=
{| evt_a := (List.map tot_map_name (fst e.(evt_a)), tot_map_net (snd e.(evt_a))) ;
   evt_l := tot_map_label e.(evt_l) ;
   evt_trace := List.map tot_map_trace_occ e.(evt_trace) |}.

Lemma tot_map_net_label_event_inf_often_occurred_conv : forall l s, inf_often (now (occurred (tot_map_label l))) (map tot_map_net_event s) -> inf_often (now (occurred l)) s.