private Range<K> coalescedRange(Range<K> range, V value) {
    Range<K> coalescedRange = range;
    Entry<Cut<K>, RangeMapEntry<K, V>> lowerEntry =
        entriesByLowerBound.lowerEntry(range.lowerBound);
    coalescedRange = coalesce(coalescedRange, value, lowerEntry);

    Entry<Cut<K>, RangeMapEntry<K, V>> higherEntry =
        entriesByLowerBound.floorEntry(range.upperBound);

  public void testLower() {
    resetWithHole();
    assertEquals(null, navigableMap.lowerEntry(a.getKey()));
    assertEquals(null, navigableMap.lowerKey(a.getKey()));
    assertEquals(a, navigableMap.lowerEntry(b.getKey()));
    assertEquals(a.getKey(), navigableMap.lowerKey(b.getKey()));
    assertEquals(a, navigableMap.lowerEntry(c.getKey()));
    assertEquals(a.getKey(), navigableMap.lowerKey(c.getKey()));
  }

  private Range<K> coalescedRange(Range<K> range, V value) {
    Range<K> coalescedRange = range;
    Entry<Cut<K>, RangeMapEntry<K, V>> lowerEntry =
        entriesByLowerBound.lowerEntry(range.lowerBound);
    coalescedRange = coalesce(coalescedRange, value, lowerEntry);

    Entry<Cut<K>, RangeMapEntry<K, V>> higherEntry =
        entriesByLowerBound.floorEntry(range.upperBound);

      assertTrue(Thread.holdsLock(mutex));
      return delegate().lastEntry();
    }

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

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

  }

  <K, V> void testNavigationAgainstExpected(
      NavigableMap<K, V> expected, NavigableMap<K, V> navigableMap, Iterable<K> keysToTest) {
    for (K key : keysToTest) {
      assertEquals(expected.lowerEntry(key), navigableMap.lowerEntry(key));
      assertEquals(expected.floorEntry(key), navigableMap.floorEntry(key));
      assertEquals(expected.ceilingEntry(key), navigableMap.ceilingEntry(key));

    public Entry<K, V2> lastEntry() {
      return transformEntry(fromMap().lastEntry());
    }

    @Override
    @CheckForNull
    public Entry<K, V2> lowerEntry(@ParametricNullness K key) {
      return transformEntry(fromMap().lowerEntry(key));
    }

    @Override
    @CheckForNull
    public K lowerKey(@ParametricNullness K key) {
      return fromMap().lowerKey(key);
    }

    public Entry<K, V2> lastEntry() {
      return transformEntry(fromMap().lastEntry());
    }

    @Override
    @CheckForNull
    public Entry<K, V2> lowerEntry(@ParametricNullness K key) {
      return transformEntry(fromMap().lowerEntry(key));
    }

    @Override
    @CheckForNull
    public K lowerKey(@ParametricNullness K key) {
      return fromMap().lowerKey(key);
    }

  }

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

  @Override
  @CheckForNull
  public K lowerKey(K key) {
    return keyOrNull(lowerEntry(key));
  }

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

        return nullableSynchronizedEntry(delegate().lastEntry(), mutex);
      }
    }

    @Override
    @CheckForNull
    public Map.Entry<K, V> lowerEntry(K key) {
      synchronized (mutex) {
        return nullableSynchronizedEntry(delegate().lowerEntry(key), mutex);
      }
    }

    @Override
    @CheckForNull
    public K lowerKey(K key) {
      synchronized (mutex) {

        return nullableSynchronizedEntry(delegate().lastEntry(), mutex);
      }
    }

    @Override
    @CheckForNull
    public Map.Entry<K, V> lowerEntry(K key) {
      synchronized (mutex) {
        return nullableSynchronizedEntry(delegate().lowerEntry(key), mutex);
      }
    }

    @Override
    @CheckForNull
    public K lowerKey(K key) {
      synchronized (mutex) {