Natural Number Multiplication Distributes over Addition

Theorem
The operation of multiplication is distributive over addition on the set of natural numbers $$\N$$:


 * $$\forall x, y, z \in \N:$$
 * $$\left({x + y}\right) z = x z + y z$$
 * $$z \left({x + y}\right) = z x + z y$$

Proof
Follows directly from the fact that the Natural Numbers form Commutative Semiring.