In Topology by Munkres, an alternative approach to proving that "an ordered set $A$ with the greatest lower bound property satisfies the least upper bound property" (this is 14c) is suggested below:
I know how to show 14a and 14b (Chapter 3). How can one use these parts to prove 14c?
For clarity of definitions:
The greatest lower bound property is defined as the property that for a set $S \subseteq A$, if $S$ has a lower bound in $A$, then its $\inf$ is also in $A$. The least upper bound property is defined similarly.