Java. TreeSet successor

I am interested in such a question: as we know, *Red-Black tree* provides efficient implementation of such operations as *successor* (the first element higher that entry) and *predecessor* , i.e. in log - time. In **Java documentation** is written that for providing such operation as successor you may merely use subSet and then took the least element in the **subSet**. But is it log-time? If it is, what is the implementation of **subSet**?(I am interested in the algorithm, so it may be just few words, not necessary code) Thanks.
I'm not sure I get the question: HashSet does have methods lower(E e) and higher(E e).

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