Class LabeledMultiParamsLabelTotalMap
 (B0 : BaseParams) (B1 : BaseParams)
 (P0 : LabeledMultiParams B0) (P1 : LabeledMultiParams B1) :=
  {    
    tot_map_label : @label B0 P0 -> @label B1 P1
  }.Class LabeledMultiParamsLabelTotalMap
 (B0 : BaseParams) (B1 : BaseParams)
 (P0 : LabeledMultiParams B0) (P1 : LabeledMultiParams B1) :=
  {    
    tot_map_label : @label B0 P0 -> @label B1 P1
  }.Definition tot_mapped_lb_net_handlers_label me src m st :=
  let '(lb, out, st', ps) := lb_net_handlers me src m st in tot_map_label lb.Definition tot_mapped_lb_input_handlers_label me inp st :=
  let '(lb, out, st', ps) := lb_input_handlers me inp st in tot_map_label lb.Class LabeledMultiParamsTotalMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : LabeledMultiParams B0) (P1 : LabeledMultiParams B1)
  (B : BaseParamsTotalMap B0 B1) 
  (N : MultiParamsNameTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (P : MultiParamsMsgTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (L : LabeledMultiParamsLabelTotalMap P0 P1) : Prop :=
  {
    tot_lb_net_handlers_eq : forall me src m st out st' ps lb, 
      lb_net_handlers (tot_map_name me) (tot_map_name src) (tot_map_msg m) (tot_map_data st) = (lb, out, st', ps)  ->
      tot_mapped_lb_net_handlers_label me src m st = lb ;
    tot_lb_input_handlers_eq : forall me inp st out st' ps lb, 
      lb_input_handlers (tot_map_name me) (tot_map_input inp) (tot_map_data st) = (lb, out, st', ps) ->
      tot_mapped_lb_input_handlers_label me inp st = lb ;
    tot_lb_label_silent_fst_snd : tot_map_label label_silent = label_silent
  }.Class LabeledMultiParamsTotalMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : LabeledMultiParams B0) (P1 : LabeledMultiParams B1)
  (B : BaseParamsTotalMap B0 B1) 
  (N : MultiParamsNameTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (P : MultiParamsMsgTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (L : LabeledMultiParamsLabelTotalMap P0 P1) : Prop :=
  {
    tot_lb_net_handlers_eq : forall me src m st out st' ps lb, 
      lb_net_handlers (tot_map_name me) (tot_map_name src) (tot_map_msg m) (tot_map_data st) = (lb, out, st', ps)  ->
      tot_mapped_lb_net_handlers_label me src m st = lb ;
    tot_lb_input_handlers_eq : forall me inp st out st' ps lb, 
      lb_input_handlers (tot_map_name me) (tot_map_input inp) (tot_map_data st) = (lb, out, st', ps) ->
      tot_mapped_lb_input_handlers_label me inp st = lb ;
    tot_lb_label_silent_fst_snd : tot_map_label label_silent = label_silent
  }.Class LabeledMultiParamsTotalMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : LabeledMultiParams B0) (P1 : LabeledMultiParams B1)
  (B : BaseParamsTotalMap B0 B1) 
  (N : MultiParamsNameTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (P : MultiParamsMsgTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (L : LabeledMultiParamsLabelTotalMap P0 P1) : Prop :=
  {
    tot_lb_net_handlers_eq : forall me src m st out st' ps lb, 
      lb_net_handlers (tot_map_name me) (tot_map_name src) (tot_map_msg m) (tot_map_data st) = (lb, out, st', ps)  ->
      tot_mapped_lb_net_handlers_label me src m st = lb ;
    tot_lb_input_handlers_eq : forall me inp st out st' ps lb, 
      lb_input_handlers (tot_map_name me) (tot_map_input inp) (tot_map_data st) = (lb, out, st', ps) ->
      tot_mapped_lb_input_handlers_label me inp st = lb ;
    tot_lb_label_silent_fst_snd : tot_map_label label_silent = label_silent
  }.Class LabeledMultiParamsTotalMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : LabeledMultiParams B0) (P1 : LabeledMultiParams B1)
  (B : BaseParamsTotalMap B0 B1) 
  (N : MultiParamsNameTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (P : MultiParamsMsgTotalMap (@unlabeled_multi_params _ P0) (@unlabeled_multi_params _ P1))
  (L : LabeledMultiParamsLabelTotalMap P0 P1) : Prop :=
  {
    tot_lb_net_handlers_eq : forall me src m st out st' ps lb, 
      lb_net_handlers (tot_map_name me) (tot_map_name src) (tot_map_msg m) (tot_map_data st) = (lb, out, st', ps)  ->
      tot_mapped_lb_net_handlers_label me src m st = lb ;
    tot_lb_input_handlers_eq : forall me inp st out st' ps lb, 
      lb_input_handlers (tot_map_name me) (tot_map_input inp) (tot_map_data st) = (lb, out, st', ps) ->
      tot_mapped_lb_input_handlers_label me inp st = lb ;
    tot_lb_label_silent_fst_snd : tot_map_label label_silent = label_silent
  }.

Theorem lb_step_failure_tot_mapped_simulation_1 : forall net net' failed failed' lb tr, @lb_step_failure _ labeled_multi_fst (failed, net) lb (failed', net') tr -> @lb_step_failure _ labeled_multi_snd (List.map tot_map_name failed, tot_map_net net) (tot_map_label lb) (List.map tot_map_name failed', tot_map_net net') (List.map tot_map_trace_occ tr).