Cartesian Product of Intersections/General Case

Theorem

 * $\displaystyle \left({ \prod_{i \mathop = 1}^n S_i }\right) \cap \left({ \prod_{i \mathop = 1}^n T_i }\right) = \prod_{i \mathop = 1}^n \left({S_i \cap T_i}\right)$