assertEquals(c, navigableMap.higherEntry(a.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(a.getKey()));
    assertEquals(c, navigableMap.higherEntry(b.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(b.getKey()));
    assertEquals(null, navigableMap.higherEntry(c.getKey()));
    assertEquals(null, navigableMap.higherKey(c.getKey()));
  }

  @CollectionSize.Require(SEVERAL)
  public void testLast() {

    assertEquals(c, navigableMap.higherEntry(a.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(a.getKey()));
    assertEquals(c, navigableMap.higherEntry(b.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(b.getKey()));
    assertEquals(null, navigableMap.higherEntry(c.getKey()));
    assertEquals(null, navigableMap.higherKey(c.getKey()));
  }

  @CollectionSize.Require(SEVERAL)
  public void testLast() {

      assertTrue(Thread.holdsLock(mutex));
      return delegate().higherEntry(key);
    }

    @Override
    public @Nullable K higherKey(K key) {
      assertTrue(Thread.holdsLock(mutex));
      return delegate().higherKey(key);
    }

    @Override
    public @Nullable Entry<K, V> lastEntry() {
      assertTrue(Thread.holdsLock(mutex));
      return delegate().lastEntry();
    }

  }

  @Override
  @CheckForNull
  public K higherKey(@ParametricNullness K key) {
    return delegate().higherKey(key);
  }

  /**
   * A sensible definition of {@link #higherKey} in terms of {@code higherEntry}. If you override
   * {@code higherEntry}, you may wish to override {@code higherKey} to forward to this
   * implementation.
   */
  @CheckForNull

  }

  @Override
  @CheckForNull
  public K higherKey(@ParametricNullness K key) {
    return delegate().higherKey(key);
  }

  /**
   * A sensible definition of {@link #higherKey} in terms of {@code higherEntry}. If you override
   * {@code higherEntry}, you may wish to override {@code higherKey} to forward to this
   * implementation.
   */
  @CheckForNull

  }

  @Override
  public @Nullable Entry<K, V> higherEntry(K key) {
    return delegate.higherEntry(checkValid(key));
  }

  @Override
  public @Nullable K higherKey(K key) {
    return delegate.higherKey(checkValid(key));
  }

  @Override
  public boolean isEmpty() {
    return delegate.isEmpty();
  }

  @Override
  public NavigableSet<K> keySet() {

  }

  @Override
  public @Nullable Entry<K, V> higherEntry(K key) {
    return delegate.higherEntry(checkValid(key));
  }

  @Override
  public @Nullable K higherKey(K key) {
    return delegate.higherKey(checkValid(key));
  }

  @Override
  public boolean isEmpty() {
    return delegate.isEmpty();
  }

  @Override
  public NavigableSet<K> keySet() {

      assertTrue(Thread.holdsLock(mutex));
      return delegate().higherEntry(key);
    }

    @Override
    public @Nullable K higherKey(K key) {
      assertTrue(Thread.holdsLock(mutex));
      return delegate().higherKey(key);
    }

    @Override
    public @Nullable Entry<K, V> lastEntry() {
      assertTrue(Thread.holdsLock(mutex));
      return delegate().lastEntry();
    }

  }

  @Override
  @CheckForNull
  public K ceilingKey(@ParametricNullness K key) {
    return Maps.keyOrNull(ceilingEntry(key));
  }

  @Override
  @CheckForNull
  public K higherKey(@ParametricNullness K key) {
    return Maps.keyOrNull(higherEntry(key));
  }

  abstract Iterator<Entry<K, V>> descendingEntryIterator();

  @Override

      return standardCeilingKey(key);
    }

    @Override
    public @Nullable Entry<K, V> higherEntry(K key) {
      return standardHigherEntry(key);
    }

    @Override
    public @Nullable K higherKey(K key) {
      return standardHigherKey(key);
    }

    @Override
    public @Nullable Entry<K, V> firstEntry() {
      return standardFirstEntry();
    }

    /*