Definition maxBeta (n : nat) (x : nat -> nat) : nat.

Theorem betaTheorem1 : forall (n : nat) (y : nat -> nat), {a : nat * nat | forall z : nat, z < n -> y z = snd (proj1_sig (modulo (coPrimeBeta z (snd a)) (gtBeta z (snd a)) (fst a)))}.