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_fun_inv_triples n f :
{ a : _ & { b | forall p, p < n -> f p = (godel_beta a b (  3*p),
godel_beta a b (1+3*p),
godel_beta a b (2+3*p)) } }.