Definition Nth := rho (.\ "nth", "n", "A";
"n" ("A" !none (.\ "a", "A"; !some "a"))
(.\"n"; ("A" !none (.\"a", "A"; "nth" "n" "A"))) ).
Definition onatenc x := match x with None => none | Some x => (lambda(lambda(1 (enc x)))) end.

(* Specifications: *)
Lemma Nth_correct A n : Nth (Encodings.enc n) (lenc A) ≡ onatenc(nth n A).
End Fix_X.