Cartesian Product is Empty iff Factor is Empty

Theorem

 * $S \times T = \O \iff S = \O \lor T = \O$

Thus:
 * $S \times \O = \O = \O \times T$

Proof
So by the Rule of Transposition:
 * $S = \O \lor T = \O \iff S \times T = \O$