Proof using.
intros f J P K Q JK PQ. cofix cf.
intros (x, s) rl. case (release_Cons rl); clear rl.
intros Pxs orR.
case orR; intro cR.
- apply R0.
* apply PQ. assumption.
* apply JK. assumption.
- apply R_tl.
* apply PQ. assumption.
* apply cf. assumption.
Qed.

Lemma release_map_conv :
forall (f: A->B) (J P: infseq A->Prop) (K Q: infseq B->Prop),
(forall s, K (map f s) -> J s) ->
(forall s, Q (map f s) -> P s) ->
forall (s: infseq A),
release K Q (map f s) -> release J P s.