then:
        Matchers.strictlyEquals(spec11.toKey(), spec11.toKey())
        Matchers.strictlyEquals(spec11.toKey(), spec11Impl1.toKey())
        Matchers.strictlyEquals(spec11Vendor1.toKey(), spec11Vendor1.toKey())
        !Matchers.strictlyEquals(spec11Vendor1.toKey(), spec11Vendor2.toKey())
        !Matchers.strictlyEquals(spec11.toKey(), spec12.toKey())
        Matchers.strictlyEquals(spec11Impl1.toKey(), spec11Impl1.toKey())

    return headMap(toKey, false);
  }

  /**
   * This method returns a {@code ImmutableSortedMap}, consisting of the entries whose keys are less
   * than (or equal to, if {@code inclusive}) {@code toKey}.
   *
   * <p>The {@link SortedMap#headMap} documentation states that a submap of a submap throws an
   * {@link IllegalArgumentException} if passed a {@code toKey} greater than an earlier {@code

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

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

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

  @Override

  @Override
  public SortedMap<K, V> subMap(@ParametricNullness K fromKey, @ParametricNullness K toKey) {
    return subMap(fromKey, true, toKey, false);
  }

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

  @Override
  public SortedMap<K, V> tailMap(@ParametricNullness K fromKey) {
    return tailMap(fromKey, true);

        Cut<C> fromKey, boolean fromInclusive, Cut<C> toKey, boolean toInclusive) {
      return subMap(
          Range.range(
              fromKey, BoundType.forBoolean(fromInclusive),
              toKey, BoundType.forBoolean(toInclusive)));
    }

    @Override
    public NavigableMap<Cut<C>, Range<C>> headMap(Cut<C> toKey, boolean inclusive) {
      return subMap(Range.upTo(toKey, BoundType.forBoolean(inclusive)));
    }

    return delegate.get(checkValid(key));
  }

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

  @Override
  public NavigableMap<K, V> headMap(K toKey, boolean inclusive) {
    return new SafeTreeMap<>(delegate.headMap(checkValid(toKey), inclusive));
  }

  @Override
  public @Nullable Entry<K, V> higherEntry(K key) {

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

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

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

  @Override

      @ParametricNullness K fromKey, @ParametricNullness K toKey) {
    return subMap(fromKey, true, toKey, false);
  }

  @Override
  public NavigableMap<K, V> subMap(
      @ParametricNullness K fromKey,
      boolean fromInclusive,
      @ParametricNullness K toKey,
      boolean toInclusive) {
    return delegate().subMap(fromKey, fromInclusive, toKey, toInclusive);
  }

  @Override

      @ParametricNullness K fromKey, @ParametricNullness K toKey) {
    return subMap(fromKey, true, toKey, false);
  }

  @Override
  public NavigableMap<K, V> subMap(
      @ParametricNullness K fromKey,
      boolean fromInclusive,
      @ParametricNullness K toKey,
      boolean toInclusive) {
    return delegate().subMap(fromKey, fromInclusive, toKey, toInclusive);
  }

  @Override

  }

  public ImmutableSortedMap<K, V> headMap(K toKey) {
    checkNotNull(toKey);
    return newView(sortedDelegate.headMap(toKey));
  }

  ImmutableSortedMap<K, V> headMap(K toKey, boolean inclusive) {
    checkNotNull(toKey);
    if (inclusive) {
      K tmp = higher(toKey);
      if (tmp == null) {
        return this;
      }
      toKey = tmp;
    }
    return headMap(toKey);
  }