Solution (source code)

= Solution

A <Sigma-1 formula> is a formula equivalent in first-order arithmetic to
$$
\exists y_1\cdots\exists y_k\,\delta,
$$
where $\delta$ is bounded. A <Pi-1 formula> is similarly equivalent to $\forall y_1\cdots\forall y_k\,\delta$ with bounded $\delta$.