Let $X = \prod_{n = 1}^N X_n$ be a D326: Cartesian product such that

(i) | $\pi_1, \ldots, \pi_N$ are each a D327: Canonical set projection on $X$ |

(ii) | $E \subseteq X$ is a D78: Subset of $X$ |

Then $(x_1, \ldots, x_N) \in E$ if and only if
\begin{equation}
x_1 \in \pi_1(E), \quad
\ldots, \quad
x_N \in \pi_N(E)
\end{equation}