Proof using.
intros P Q J K PQ JK s unJP.
induction unJP.
- apply U0, PQ; assumption.
- apply U_next.
* apply JK; assumption.
* assumption.
Qed.

(* Specifications: *)
Lemma release_monotonic :
forall (P Q J K: infseq T -> Prop),
(forall s, P s -> Q s) -> (forall s, J s -> K s) ->
forall s, release J P s -> release K Q s.