General Associative Law for Ordinal Sum/Proof 2

Theorem
Let $x$ be a finite ordinal.

Let $\left\langle{a_i}\right\rangle$ be a sequence of ordinals.

Then:


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

Proof
From Ordinal Addition is Associative we have that:
 * $\forall a, b, c \in \operatorname{On}: a + \left({b + c}\right) = \left({a + b}\right) + c$

The result follows directly from the General Associativity Theorem.