Order Type Multiplication Distributes over Addition

Theorem
Let $\alpha$, $\beta$ and $\gamma$ be order types of ordered sets.

Then:
 * $\alpha \cdot \paren {\beta + \gamma} = \paren {\alpha \cdot \beta} + \paren {\alpha \cdot \gamma}$

where:
 * $+$ denotes order type addition
 * $\cdot$ denotes order type multiplication.