Cartesian Product Distributes over Set Difference

Theorem
Cartesian product is distributive over set difference:


 * $S \times \left({T_1 \setminus T_2}\right) = \left({S \times T_1}\right) \setminus \left({S \times T_2}\right)$
 * $\left({T_1 \setminus T_2}\right) \times S = \left({T_1 \times S}\right) \setminus \left({T_2 \times S}\right)$

Proof
The proof of the other result is similar.