Proof using.
intros P Q eP eQ. cofix cf.
intros (x1, s1) (x2, s2) e rl1. case (release_Cons rl1). intros Qx orR. case orR; intro orRx.
- apply R0.
* eapply eQ; eassumption.
* eapply eP; eassumption.
- apply R_tl.
* eapply eQ; eassumption.
* simpl. apply cf with s1; trivial. case (exteq_inversion e); trivial.
Qed.

(* Specifications: *)
Lemma extensional_eventually :
forall (P: infseq T -> Prop),
extensional P -> extensional (eventually P).