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

(i)	$\bigcup_{j \in J} X_j$ is the D77: Set union of $X = \{ X_j \}_{j \in J}$

The cartesian product of $X = \{ X_j \}_{j \in J}$ is the D11: Set $$\begin{equation} \prod_{j \in J} X_j : = \left\{ x : J \to \bigcup_{j \in J} X_j \mid \forall \, j \in J : x_j \in X_j \right\} \end{equation}$$