SortedMap<String, Integer> headMap = map.headMap("a");
    assertTrue(headMap instanceof SynchronizedSortedMap);
    assertSame(mutex, ((SynchronizedSortedMap<String, Integer>) headMap).mutex);
  }

  public void testHeadMap_K_B() {
    NavigableMap<String, Integer> map = create();
    NavigableMap<String, Integer> headMap = map.headMap("a", true);
    assertTrue(headMap instanceof SynchronizedNavigableMap);

    SortedMap<String, Integer> filtered = Maps.filterEntries(unfiltered, CORRECT_LENGTH);

    assertEquals(ImmutableMap.of("banana", 6), filtered.headMap("dog"));
    assertEquals(ImmutableMap.of(), filtered.headMap("banana"));
    assertEquals(ImmutableMap.of("banana", 6, "dog", 3), filtered.headMap("emu"));

    assertEquals(ImmutableMap.of("banana", 6), filtered.subMap("banana", "dog"));

    TreeBasedTable<String, Integer, Character> table = makeTable();
    populateTable(table);
    return table.rowMap().headMap("x");
  }

  @Override
  protected Map<String, Map<Integer, Character>> makeEmptyMap() {
    return makeTable().rowMap().headMap("x");
  }

  @Override
  protected String getKeyNotInPopulatedMap() {
    return "z";
  }

   * A sensible definition of {@link #lowerEntry} in terms of the {@code lastEntry()} of {@link
   * #headMap(Object, boolean)}. If you override {@code headMap}, you may wish to override {@code
   * lowerEntry} to forward to this implementation.
   */
  @CheckForNull
  protected Entry<K, V> standardLowerEntry(@ParametricNullness K key) {
    return headMap(key, false).lastEntry();
  }

  @Override
  @CheckForNull

  }

  @Override
  @ParametricNullness
  public K firstKey() {
    return delegate().firstKey();
  }

  @Override
  public SortedMap<K, V> headMap(@ParametricNullness K toKey) {
    return delegate().headMap(toKey);
  }

  @Override
  @ParametricNullness
  public K lastKey() {
    return delegate().lastKey();
  }

  @Override

      extends AbstractNavigableMap<Cut<C>, Range<C>> {
    private final NavigableMap<Cut<C>, Range<C>> rangesByLowerBound;

    /**
     * upperBoundWindow represents the headMap/subMap/tailMap view of the entire "ranges by upper
     * bound" map; it's a constraint on the *keys*, and does not affect the values.
     */
    private final Range<Cut<C>> upperBoundWindow;

      return standardDescendingKeySet();
    }

    @Override
    public K firstKey() {
      return standardFirstKey();
    }

    @Override
    public SortedMap<K, V> headMap(K toKey) {
      return standardHeadMap(toKey);
    }

    @Override
    public K lastKey() {
      return standardLastKey();
    }

    @Override
    public SortedMap<K, V> tailMap(K fromKey) {

  }

  @CollectionSize.Require(absent = ZERO)
  public void testHeadMapExclusive() {
    assertFalse(navigableMap.headMap(a.getKey(), false).containsKey(a.getKey()));
  }

  @CollectionSize.Require(absent = ZERO)
  public void testHeadMapInclusive() {
    assertTrue(navigableMap.headMap(a.getKey(), true).containsKey(a.getKey()));
  }

  @CollectionSize.Require(absent = ZERO)
  public void testTailMapExclusive() {

        assertThat(navigableMap.headMap(key, inclusive).entrySet())
            .containsExactlyElementsIn(expected.headMap(key, inclusive).entrySet())
            .inOrder();
        assertThat(navigableMap.tailMap(key, inclusive).entrySet())
            .containsExactlyElementsIn(expected.tailMap(key, inclusive).entrySet())
            .inOrder();
        assertThat(navigableMap.headMap(key, inclusive).descendingMap().entrySet())

    extends AbstractImmutableSortedMapMapInterfaceTest<String, Integer> {
  @Override
  protected SortedMap<String, Integer> makePopulatedMap() {
    return ImmutableSortedMap.of("a", 1, "b", 2, "c", 3, "d", 4, "e", 5).headMap("c", true);
  }

  @Override
  protected String getKeyNotInPopulatedMap() {
    return "d";
  }

  @Override
  protected Integer getValueNotInPopulatedMap() {
    return 4;
  }