From Undecidability.L Require Import Tactics Encodings DecidableRecognisable.
Implicit Type p : term -> Prop.
Implicit Types s t u : term.
(** * Reduction lemma and Rice’s theorem *)
(** ** Closedness is decidable *)
Definition Leb := Eval cbn in
rho (.\ "leb", "m", "n"; "m" !T (.\ "m'"; "n" !F (.\ "n'"; "leb" "m'" "n'"))).
Hint Unfold Leb: cbv.

Lemma Leb_correct m n : Leb (enc m) (enc n) ≡ benc (leb m n).
Hint Rewrite Leb_correct : Lcorrect.