How to remove, from a set, a single element that satisfies a property? How do I pick a single element from a set that satisfies a property? For instance, I want to write something like this:
$$S = S - \{s \in S \ | \ s \text{ is pretty}\}$$
But with $\{s \in S \ | \ s \text{ is pretty}\}$ I want to pick a single element (any of the pretty ones).
Edit: If possible, the answer should be in a syntax similar to the definition of a set.

You say "Let $p$ be a pretty element of $S$, and let $S' = S - \{p\}$".
Of course you have to show first that $S$ does have at least one pretty element.
