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).

(* Specifications: *)
Lemma in_msg_filterMap_pt_map_msg : forall l m' m0, pt_map_msg m0 = Some m' -> In m0 l -> In m' (filterMap pt_map_msg l).
Lemma in_filterMap_pt_map_msg_in_msg : forall l m0 m1, pt_map_msg m0 = Some m1 -> In m1 (filterMap pt_map_msg l) -> In m0 l.
Lemma in_all_before_pt_map_msg : forall l m0 m1 m'0 m'1, pt_map_msg m0 = Some m'0 -> pt_map_msg m1 = Some m'1 -> before_all m'0 m'1 (filterMap pt_map_msg l) -> before_all m0 m1 l.
Lemma count_occ_filterMap_pt_map_msg_eq : forall l m' m0, pt_map_msg m0 = Some m' -> count_occ msg_eq_dec (filterMap pt_map_msg l) m' = count_occ msg_eq_dec l m0.
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'.