(a, b) -> {
          count.incrementAndGet();
          assertThat(a.equals(String.valueOf(b))).isTrue();
        });
    assertThat(count.get()).isEqualTo(100000);
    // of course, this test doesn't prove that anything actually happened in parallel...
  }

  // TODO(kevinb): switch to importing Truth's assertThat(DoubleStream) if we get that added
  private static IterableSubject assertThatDoubleStream(DoubleStream stream) {

      // even though K doesn't explicitly implement Comparable.
      comparator = (Comparator<? super K>) NATURAL_ORDER;
    }
    if (map instanceof ImmutableSortedMap) {
      // TODO(kevinb): Prove that this cast is safe, even though
      // Collections.unmodifiableSortedMap requires the same key type.
      @SuppressWarnings("unchecked")
      ImmutableSortedMap<K, V> kvMap = (ImmutableSortedMap<K, V>) map;

        verifyScenario(alteration.mutate(scenario), level + 1);
      }
    }
  }

  /**
   * An aggregation of an ordering with a list (of size > 1) that should prove to be in strictly
   * increasing order according to that ordering.
   */
  private static class Scenario<T extends @Nullable Object> {
    final Ordering<T> ordering;
    final List<T> strictlyOrderedList;

        verifyScenario(alteration.mutate(scenario), level + 1);
      }
    }
  }

  /**
   * An aggregation of an ordering with a list (of size > 1) that should prove to be in strictly
   * increasing order according to that ordering.
   */
  private static class Scenario<T extends @Nullable Object> {
    final Ordering<T> ordering;
    final List<T> strictlyOrderedList;

    assertEquals("bar", Iterables.getLast(iterable, "qux"));
  }

  /**
   * {@link ArrayList} extension that forbids the use of {@link Collection#iterator} for tests that
   * need to prove that it isn't called.
   */
  private static class DiesOnIteratorArrayList extends ArrayList<String> {
    /** @throws UnsupportedOperationException all the time */
    @Override
    public Iterator<String> iterator() {

    }
  }

  /*
   * Preconditions.checkNotNull is *intended* for performing eager null checks on parameters that a
   * nullness checker can already "prove" are non-null. That means that the first parameter to
   * checkNotNull *should* be annotated to require it to be non-null.
   *
   * However, for a variety of reasons, Google developers have written a ton of code over the past

        return true;
      }
    }
    throw new AssertionError();
  }

  /*
   * If n <= millerRabinBases[i][0], then testing n against bases millerRabinBases[i][1..] suffices
   * to prove its primality. Values from miller-rabin.appspot.com.
   *
   * NOTE: We could get slightly better bases that would be treated as unsigned, but benchmarks
   * showed negligible performance improvements.
   */

    public int hashCode() {
      // Warning: this is broken if size() == 0, so it is critical that we
      // substitute an empty ImmutableSet to the user in place of this

      // It's a weird formula, but tests prove it works.
      int adjust = size() - 1;
      for (int i = 0; i < axes.size(); i++) {
        adjust *= 31;
        adjust = ~~adjust;
        // in GWT, we have to deal with integer overflow carefully
      }

  }

  private static <K, V> ImmutableSortedMap<K, V> copyOfInternal(
      Map<? extends K, ? extends V> map, Comparator<? super K> comparator) {

    if (map instanceof ImmutableSortedMap) {
      // TODO: Prove that this cast is safe, even though
      // Collections.unmodifiableSortedMap requires the same key type.
      @SuppressWarnings("unchecked")
      ImmutableSortedMap<K, V> kvMap = (ImmutableSortedMap<K, V>) map;

      // even though K doesn't explicitly implement Comparable.
      comparator = (Comparator<? super K>) NATURAL_ORDER;
    }
    if (map instanceof ImmutableSortedMap) {
      // TODO(kevinb): Prove that this cast is safe, even though
      // Collections.unmodifiableSortedMap requires the same key type.
      @SuppressWarnings("unchecked")
      ImmutableSortedMap<K, V> kvMap = (ImmutableSortedMap<K, V>) map;