proposition: Lemma betaTheorem : forall (n : nat) (y : nat -> nat), {a : nat * nat | forall z : nat, z < n -> y z = beta (fst a) (snd a) z}.
proof: Proof. intros n y; destruct (betaTheorem1 n y) as [x e]. unfold beta; now exists x. Qed.
imports: Arith Wf_nat ZArith Peano_dec ZArith_dec NatAux ZCAux ZCmisc ZSum Pmod Ppow