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

(* Specifications: *)
Lemma maxBetaLe : forall (n : nat) (x : nat -> nat) (i : nat), i < n -> x i <= maxBeta n x.
Theorem divProd2 : forall (n : nat) (x : nat -> nat) (i : nat), i <= n -> Divides (prod i x) (prod n x).
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)))}.