Cartesian Product Distributes over Set Difference

Theorem
Cartesian Product is distributive over Set Difference:


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

Proof
$$ $$ $$ $$ $$

The proof of the other result is similar.