From Undecidability.L Require Import Interpreter Encodings.
Definition test (u : term) := forall n, u (enc n) ▷ T \/ u (enc n) ▷ F.
Definition satis u n := u (enc n) ▷ T.
Hint Unfold test.
Section fix_u.
Variable u : term.
Hypothesis proc_u : proc u.
Hypothesis test_u : test u.
Definition H := rho (.\"H", "n", "u"; "u" "n" (.\ "_"; "n") (.\ "_"; "H" (!Succ "n") "u") !I).
Hint Unfold H : cbv.

Lemma H_n_Sn n : ok (S n) -> ok n.
Proof with eauto.