Section fractran_dio.
Notation "l /F/ x → y" := (fractran_step l x y) (at level 70, no associativity).
(* Fractran step is a diophantine relation, by induction on l *)

Lemma dio_rel_fractran_step l x y : 𝔻F x -> 𝔻F y -> 𝔻R (fun ν => l /F/ x ν → y ν).