Local Arguments update {_} {_} _ _ _ _ _ : simpl never.
Set Implicit Arguments.
Class LabeledMultiParamsLabelTotalMap
(B0 : BaseParams) (B1 : BaseParams)
(P0 : LabeledMultiParams B0) (P1 : LabeledMultiParams B1) :=
{
tot_map_label : @label B0 P0 -> @label B1 P1
}.
Section LabeledTotalMapDefs.
Context {base_fst : BaseParams}.
Context {base_snd : BaseParams}.
Context {labeled_multi_fst : LabeledMultiParams base_fst}.
Context {labeled_multi_snd : LabeledMultiParams base_snd}.
Context {label_map : LabeledMultiParamsLabelTotalMap labeled_multi_fst labeled_multi_snd}.
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.
End LabeledTotalMapDefs.
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
}.
Section TotalMapExecutionSimulations.
Context {base_fst : BaseParams}.
Context {base_snd : BaseParams}.
Context {labeled_multi_fst : LabeledMultiParams base_fst}.
Context {labeled_multi_snd : LabeledMultiParams base_snd}.
Context {base_map : BaseParamsTotalMap base_fst base_snd}.
Context {name_map : MultiParamsNameTotalMap (@unlabeled_multi_params _ labeled_multi_fst) (@unlabeled_multi_params _ labeled_multi_snd)}.
Context {msg_map : MultiParamsMsgTotalMap (@unlabeled_multi_params _ labeled_multi_fst) (@unlabeled_multi_params _ labeled_multi_snd)}.
Context {label_map : LabeledMultiParamsLabelTotalMap labeled_multi_fst labeled_multi_snd}.
Context {name_map_bijective : MultiParamsNameTotalMapBijective name_map}.
Context {multi_map_congr : MultiParamsTotalMapCongruency base_map name_map msg_map}.
Context {multi_map_lb_congr : LabeledMultiParamsTotalMapCongruency base_map name_map msg_map label_map}.
Hypothesis tot_map_label_injective :
forall l l', tot_map_label l = tot_map_label l' -> l = l'.
(* lb_step_failure *)

(* Specifications: *)
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).