Proof using name_map_bijective multi_map_lb_congr multi_map_congr.
cofix c.
move => s H_exec.
rewrite -tot_map_net_event_map_unfold {1}/tot_map_net_event /=.
inversion H_exec; subst => /=.
rewrite -tot_map_net_event_map_unfold /= /tot_map_net_event /=.
apply: (@Cons_lb_step_exec _ _ _ _ _ _ (List.map tot_map_trace_occ tr)) => /=.
- apply: lb_step_failure_tot_mapped_simulation_1.
have <-: evt_a e = (fst (evt_a e), snd (evt_a e)) by destruct e, evt_a.
by have <-: evt_a e' = (fst (evt_a e'), snd (evt_a e')) by destruct e', evt_a.
- simpl in *.
find_rewrite.
by rewrite map_app.
- set e0 := {| evt_a := _ ; evt_l := _ ; evt_trace := _ |}.
have ->: e0 = tot_map_net_event e' by [].
pose s' := Cons e' s0.
rewrite (tot_map_net_event_map_unfold s').
exact: c.
Qed.

(* Specifications: *)
Lemma tot_map_net_label_event_inf_often_occurred :
forall l s,
inf_often (now (occurred l)) s ->
inf_often (now (occurred (tot_map_label l))) (map tot_map_net_event s).