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 lb_step_trace_execution_lb_step_failure_tot_map_net_infseq : forall s, lb_step_execution lb_step_failure s -> lb_step_execution lb_step_failure (map tot_map_net_event s).