Proof with eauto; try now intuition.
intros. destruct H0 as [u [H0 H0']]. eapply Rice.
- intros. hnf. intuition. eapply H. exact H2. eauto. eauto. split; intros (? & ?); exists x; firstorder.
- eauto.
- eauto.
- firstorder.
Qed.

Lemma rec_total_cls : ~ recognisable (fun s => closed s /\ ~forall t, pi s t).