Proof using overlay_map_congr name_map_bijective multi_map_lb_congr multi_map_congr label_eq_dec fail_msg_map_congr.
case => e s H_star H_exec.
apply: step_ordered_failure_star_lb_step_execution; first exact: pt_map_onet_hd_step_ordered_failure_star.
exact: lb_step_execution_lb_step_ordered_failure_pt_map_onet_infseq.
Qed.
(* lb_step_ordered_dynamic_failure *)

Theorem lb_step_ordered_dynamic_failure_pt_mapped_simulation_1_non_silent :
forall net net' failed failed' lb tr,
tot_map_label lb <> label_silent ->
@lb_step_ordered_dynamic_failure _ labeled_multi_fst (failed, net) lb (failed', net') tr ->
@lb_step_ordered_dynamic_failure _ labeled_multi_snd (List.map tot_map_name failed, pt_map_odnet net) (tot_map_label lb) (List.map tot_map_name failed', pt_map_odnet net') (filterMap pt_map_trace_ev tr).