Corollary step_ordered_dynamic_failure_pt_mapped_simulation_star_1 :
  forall net failed tr,
    @step_ordered_dynamic_failure_star _ _ overlay_fst new_msg_fst fail_msg_fst step_ordered_dynamic_failure_init (failed, net) tr ->
    @step_ordered_dynamic_failure_star _ _ overlay_snd new_msg_snd fail_msg_snd step_ordered_dynamic_failure_init (map tot_map_name failed, pt_map_odnet net) (filterMap pt_map_trace_ev tr).

Lemma hd_error_filterMap_pt_map_msg : forall l m' m0, pt_map_msg m0 = Some m' -> hd_error l = Some m0 -> hd_error (filterMap pt_map_msg l) = Some m'.