Class of All Ordinals is G-Tower
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Theorem
Let $\On$ denote the class of all ordinals.
Let $g$ be the successor mapping:
- $\forall x \in \On: \map g x = x \cup \set x$
Then $\On$ is a $g$-tower.
Proof
From Successor Mapping is Progressing, $g$ is a progressing mapping.
From Class of All Ordinals is Minimally Superinductive over Successor Mapping, $\On$ is superinductive over $g$.
Hence the result by definition of $g$-tower.
$\blacksquare$