getMap().remove(k0());
    expectMissing(e0());
  }

  @MapFeature.Require(SUPPORTS_REMOVE)
  @CollectionSize.Require(absent = ZERO)
  public void testRemoveKeyFromKeySetRemovesFromInverse() {
    getMap().keySet().remove(k0());
    expectMissing(e0());
  }

  @MapFeature.Require(SUPPORTS_REMOVE)
  @CollectionSize.Require(absent = ZERO)
  public void testRemoveFromValuesRemovesFromInverse() {

    for (Entry<K, V> entry : getSampleElements()) {
      assertTrue(multimap().keySet().contains(entry.getKey()));
    }
  }

  @CollectionSize.Require(absent = ZERO)
  @MapFeature.Require(ALLOWS_NULL_KEYS)
  public void testKeySetContainsNullKeyPresent() {
    initMultimapWithNullKey();
    assertTrue(multimap().keySet().contains(null));
  }

  @MapFeature.Require(ALLOWS_NULL_KEY_QUERIES)

  private final transient RegularImmutableSortedSet<K> keySet;
  private final transient ImmutableList<V> valueList;
  @CheckForNull private transient ImmutableSortedMap<K, V> descendingMap;

  ImmutableSortedMap(RegularImmutableSortedSet<K> keySet, ImmutableList<V> valueList) {
    this(keySet, valueList, null);
  }

  ImmutableSortedMap(
      RegularImmutableSortedSet<K> keySet,
      ImmutableList<V> valueList,

    create().putAll(new HashMap<String, Integer>());
  }

  public void testKeySet() {
    Map<String, Integer> map = create();
    Set<String> keySet = map.keySet();
    assertTrue(keySet instanceof SynchronizedSet);
    assertSame(mutex, ((SynchronizedSet<?>) keySet).mutex);
  }

  public void testValues() {
    Map<String, Integer> map = create();
    Collection<Integer> values = map.values();

    CacheTesting.warmUp(cache, 0, 10);
    Set<Integer> keySet = cache.asMap().keySet();
    assertThat(keySet).containsExactly(0, 1, 2, 3, 4, 5, 6, 7, 8, 9);

    // re-order
    getAll(cache, asList(0, 1, 2));
    CacheTesting.drainRecencyQueues(cache);
    assertThat(keySet).containsExactly(3, 4, 5, 6, 7, 8, 9, 0, 1, 2);

    // evict 3, 4, 5
    getAll(cache, asList(10, 11, 12));

      return delegate;
    }

    @Override
    public Set<K> keySet() {
      return new ForwardingSet<K>() {
        @Override
        protected Set<K> delegate() {
          return delegate.keySet();
        }

        @Override
        public Iterator<K> iterator() {
          return Iterators.unmodifiableIterator(delegate.keySet().iterator());
        }

        @Override

    SortedSet<@Nullable String> keySet = multimap.keySet();

    assertEquals(null, keySet.first());
    assertEquals("google", keySet.last());
    assertEquals(StringLength.COMPARATOR, keySet.comparator());
    assertEquals(Sets.<@Nullable String>newHashSet(null, "tree"), keySet.headSet("yahoo"));
    assertEquals(newHashSet("google"), keySet.tailSet("yahoo"));

  protected final void assertInvariants(Map<K, V> map) {
    Set<K> keySet = map.keySet();
    Collection<V> valueCollection = map.values();
    Set<Entry<K, V>> entrySet = map.entrySet();

    assertEquals(map.size() == 0, map.isEmpty());
    assertEquals(map.size(), keySet.size());
    assertEquals(keySet.size() == 0, keySet.isEmpty());
    assertEquals(!keySet.isEmpty(), keySet.iterator().hasNext());

    int expectedKeySetHash = 0;

  protected final void assertInvariants(Map<K, V> map) {
    Set<K> keySet = map.keySet();
    Collection<V> valueCollection = map.values();
    Set<Entry<K, V>> entrySet = map.entrySet();

    assertEquals(map.size() == 0, map.isEmpty());
    assertEquals(map.size(), keySet.size());
    assertEquals(keySet.size() == 0, keySet.isEmpty());
    assertEquals(!keySet.isEmpty(), keySet.iterator().hasNext());

    int expectedKeySetHash = 0;

    assertEquals("[" + joiner.join(map.keySet()) + "]", map.keySet().toString());
    assertEquals("[" + joiner.join(map.values()) + "]", map.values().toString());

    assertEquals(newHashSet(map.entrySet()), map.entrySet());
    assertEquals(newHashSet(map.keySet()), map.keySet());
  }