Distinct Lower Sections of Well-Ordered Class are not Order Isomorphic

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Let $\struct {A, \preccurlyeq}$ be a well-ordered class.

Let $L_1$ and $L_2$ be distinct lower sections of $\struct {A, \preccurlyeq}$.

Then $L_1$ and $L_2$ are not order isomorphic with respect to $\preccurlyeq$.


A lower section of $A$ is a subclass of $A$.

Hence by definition of well-ordered class. $L_1$ and $L_2$ are themselves well-ordered classes.

We have $L_1 \ne L_2$.

The result follows from