Section Godel_beta.
(* Gödel Beta function and its "inverse" as a Coq function for the reduction H10C -> termination of one particular µ-rec function *)
Definition godel_beta a b n := rem a (S ((S n)*b)).

Theorem godel_beta_inv n (v : vec nat n) :
{ a : nat & { b | forall p, godel_beta a b (pos2nat p) = vec_pos v p } }.