General Associative Law for Ordinal Sum

Theorem
Let $x$ be a finite ordinal.

Let $\sequence {a_i}$ be a sequence of ordinals.

Then:


 * $\ds \sum_{i \mathop = 1}^{x + 1} a_i = a_1 + \sum_{i \mathop = 1}^x a_{i + 1}$