Product of Subset with Union

Theorem
Let $\left({G, \circ}\right)$ be an algebraic structure.

Let $X, Y, Z \subseteq G$.

Then:


 * $X \circ \left({Y \cup Z}\right) = \left({X \circ Y}\right) \cup \left({X \circ Z}\right)$


 * $\left({Y \cup Z}\right) \circ X = \left({Y \circ X}\right) \cup \left({Z \circ X}\right)$

where $X \circ Y$ denotes the subset product of $X$ and $Y$.