Proof using tot_map_label_injective.
move => l.
apply: always_map_conv.
apply: eventually_map_conv => //.
- exact: extensional_now.
- exact: extensional_now.
- case => e s.
rewrite /= /occurred /=.
move => H_eq.
exact: tot_map_label_injective.
Qed.
Hypothesis lb_step_ordered_failure_strong_fairness_enabled_pt_map_onet_eventually :
forall l, tot_map_label l <> label_silent ->
forall s, lb_step_execution lb_step_ordered_failure s ->
strong_fairness lb_step_ordered_failure label_silent s ->
enabled lb_step_ordered_failure (tot_map_label l) (pt_map_onet_event (hd s)) ->
eventually (now (enabled lb_step_ordered_failure l)) s.

(* Specifications: *)
Lemma pt_map_onet_tot_map_labeled_event_inf_often_enabled :
forall l, tot_map_label l <> label_silent ->
forall s, lb_step_execution lb_step_ordered_failure s ->
strong_fairness lb_step_ordered_failure label_silent s ->
inf_often (now (enabled lb_step_ordered_failure (tot_map_label l))) (map pt_map_onet_event s) ->
inf_often (now (enabled lb_step_ordered_failure l)) s.