Cartesian Product Distributes over Union

Theorem
Cartesian Product is distributive over union:


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

Proof
$$ $$ $$ $$ $$ $$

Thus $$S \times \left({T_1 \cup T_2}\right) = \left({S \times T_1}\right) \cup \left({S \times T_2}\right)$$.

The other result is proved similarly.