Let $E_1, \, \ldots, \, E_N$ each be a D11: Set such that

(i)	$\bigcup_{n = 1}^N E_n$ is a D77: Set union for $E_1, \, \ldots, \, E_N$

Then \begin{equation} E_1 \subseteq \bigcup_{n = 1}^N E_n, \quad E_2 \subseteq \bigcup_{n = 1}^N E_n, \quad \ldots, \quad E_N \subseteq \bigcup_{n = 1}^N E_n \end{equation}

Let $E_1, \, \ldots, \, E_N$ each be a D11: Set such that

(i)	$\cup E$ is a D77: Set union for $E = (E_1, \, \ldots, \, E_N)$

Then \begin{equation} E_1 \subseteq \cup E, \quad E_2 \subseteq \cup E, \quad \ldots, \quad E_N \subseteq \cup E \end{equation}