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) |}.

Theorem lb_step_ordered_failure_tot_mapped_simulation_1 : forall net net' failed failed' lb tr, @lb_step_ordered_failure _ labeled_multi_fst (failed, net) lb (failed', net') tr -> @lb_step_ordered_failure _ labeled_multi_snd (List.map tot_map_name failed, tot_map_onet net) (tot_map_label lb) (List.map tot_map_name failed', tot_map_onet net') (List.map tot_map_trace tr).