Definition:Proper Lower Section (Class Theory)

Definition
Let $A$ be a class under a total ordering $\preccurlyeq$.

Let $L$ be a lower section of $A$ such that:
 * $L \ne \O$
 * $L \ne A$

Then $L$ is known as a proper lower section of $A$ (by $L$).

Also see

 * Definition:Lower Section (Class Theory)