Section hoas. Import HOAS_Notations.
Definition Eval :term := Eval cbn in
(λ u, !!(ext eva)
(!!mu (λ n, !!(ext doesHaltIn) u n)) u !!I !!I).
End hoas.
Proof with Lproc.
intros p H. rewrite Eval_correct in H;try Lproc. destruct H as [n [v [R [eq lv]]]]. subst t.
eexists. split. reflexivity. Lrewrite in R. apply enc_extinj in R. apply eva_equiv in R. split. apply equiv_lambda;try Lproc.  assumption. assumption.
Qed.

Lemma Eval_converges s : converges s <-> converges (Eval (ext s)).