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.

Lemma seval_Eval n (s t:term): seval n s t -> Eval (ext s) == (ext t).