Let $X_1, \ldots, X_N$ each be a D11: Set.
Let $\pi : \{ 1, \ldots, N \} \to \{ 1, \ldots, N \}$ be a D353: Set automorphism.
Let $\pi : \{ 1, \ldots, N \} \to \{ 1, \ldots, N \}$ be a D353: Set automorphism.
Then
\begin{equation}
X_1 \cap X_2 \cap \cdots \cap X_N
= X_{\pi(1)} \cap X_{\pi(2)} \cap \cdots \cap X_{\pi(N)}
\end{equation}