Section df_seq.
(* If R is a diophantine binary relation then the predicate fun c q n => is_seq R c q n is also diophantine. It states that the first (n+1) digits of c in base q say x0,...,xn form a R-sequence, ie x0 R x1 R ... R xn *)
Variable (R : nat -> nat -> Prop) (HR : 𝔻R (fun ν => R (ν 1) (ν 0))).

Theorem dio_rel_is_seq c q n : 𝔻F c -> 𝔻F q -> 𝔻F n
-> 𝔻R (fun ν => is_seq R (c ν) (q ν) (n ν)).