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.

Then \begin{equation} \bigcap_{n = 1}^N X_n = \bigcap_{n = 1}^N X_{\pi(n)} \end{equation}

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.

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}