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static class DerivedSet<A> extends AbstractSet<A> {
  Set<A> base;
  Set<A> additions = new HashSet;
  
  *() {}
  *(Set<A> *base) {}
  *(Set<A> *base, Set<A> *additions) {}
  
  public int size() { ret base.size()+additions.size(); }
  public Iterator<A> iterator() { fail(); }
  public bool contains(O o) { ret base.contains(o) || additions.contains(o); }
  
  public bool add(A a) {
    ret !base.contains(a) && additions.add(a);
  }
  
  // does not remove from base set, only from additions
  public bool remove(O o) { ret additions.remove(o); }
  
  O mutex() { ret collectionMutex(additions); }
}