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    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);

   * 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

    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"));

   * 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

    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"));

    }
  }

  @Override
  @CheckForNull
  public Entry<K, V> lowerEntry(@ParametricNullness K key) {
    return headMap(key, false).lastEntry();
  }

  @Override
  @CheckForNull
  public Entry<K, V> floorEntry(@ParametricNullness K key) {
    return headMap(key, true).lastEntry();
  }

  @Override
  @CheckForNull
  public Entry<K, V> ceilingEntry(@ParametricNullness K key) {

  }

  @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

    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";
  }

    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";
  }