Proof using.
move => step silent.
rewrite /extensional /strong_fairness /inf_enabled /inf_occurred /=.
move => s1 s2 H_eq H_s1 l' H_neq' H_en.
have H_s1l := H_s1 l'.
move: H_s1l.
set s1i := inf_often (now (occurred _)) s1.
move => H_s1l.
suff H_suff: s1i.
move: H_suff.
apply extensional_inf_often => //.
exact: extensional_now.
apply: H_s1l => {s1i}; first by [].
move: H_en.
apply: extensional_inf_often; last exact: exteq_sym.
exact: extensional_now.
Qed.

Lemma weak_fairness_invar :
forall step e silent s, weak_fairness step silent (Cons e s) -> weak_fairness step silent s.