Let $E_j$ be a D11: Set for each $j \in J$ such that

(i)	$\bigcap_{j \in J} E_j$ is a D76: Set intersection for $\{ E_j \}_{j \in J}$

Then \begin{equation} \forall \, i \in J : \bigcap_{j \in J} E_j \subseteq E_i \end{equation}

Let $E_j$ be a D11: Set for each $j \in J$ such that

(i)	$\cap E$ is a D76: Set intersection for $E = \{ E_j \}_{j \in J}$

Then \begin{equation} \forall \, j \in J : \cap E \subseteq E_j \end{equation}