Proof using multi_map_lb_congr lb_step_ordered_failure_strong_fairness_enabled_pt_map_onet_eventually label_tot_mapped.
move => s.
rewrite /strong_fairness => H_exec H_fair l H_neq H_en.
have [l' H_l] := label_tot_mapped l.
rewrite H_l.
apply pt_map_onet_tot_map_label_event_inf_often_occurred.
apply H_fair; first by move => H_eq; rewrite H_eq pt_lb_label_silent_fst_snd in H_l.
rewrite H_l in H_en.
unfold inf_enabled in *.
apply: pt_map_onet_tot_map_labeled_event_inf_often_enabled => //.
move => H_eq.
by rewrite -H_l in H_eq.
Qed.

(* Specifications: *)
Lemma pt_map_onet_tot_map_label_event_state_weak_fairness :
forall s, lb_step_execution lb_step_ordered_failure s ->
weak_fairness lb_step_ordered_failure label_silent s ->
weak_fairness lb_step_ordered_failure label_silent (map pt_map_onet_event s).