Proof using.
unfold strong_fairness. unfold inf_enabled, inf_occurred, inf_often.
intros step e silent s fair l neq alev.
assert (alevt_es: always (eventually (now (enabled step l))) (Cons e s)).
constructor.
constructor 2. destruct alev; assumption.
simpl. assumption.
clear alev. generalize (fair l neq alevt_es); clear fair alevt_es.
intro fair; case (always_Cons fair); trivial.
Qed.

Lemma strong_fairness_extensional :
forall step silent, extensional (strong_fairness step silent).