Rank of Ordinal

Theorem
Let $x$ be an ordinal.

Let $\operatorname{rank} \left({ x }\right)$ denote the rank of $x$.

Then:


 * $\operatorname{rank} \left({ x }\right) = x$

Proof
The proof shall proceed by Transfinite Induction (Strong Induction) on $x$.

Suppose $\forall y \in x: \operatorname{rank} \left({ y }\right) = y$.

Then: