{* ../../docs_src/dependencies/tutorial001_02_an_py310.py hl[12,16,21] *}

/// tip

This is just standard Python, it's called a "type alias", it's actually not specific to **FastAPI**.

But because **FastAPI** is based on the Python standards, including `Annotated`, you can use this trick in your code. 😎

///

   * this graph.
   *
   * <p>This is equal to the union of {@link #predecessors(Object)} and {@link #successors(Object)}.
   *
   * <p>If {@code node} is removed from the graph after this method is called, the {@code Set}
   * {@code view} returned by this method will be invalidated, and will throw {@code
   * IllegalStateException} if it is accessed in any way, with the following exceptions:
   *
   * <ul>

    assertEquals(4, list.lastIndexOf("b"));
  }

  public void testCopyOfDefensiveCopy() {
    // Depending on JDK version, either toArray() or toArray(T[]) may be called... use this class
    // rather than mocking to ensure that one of those methods is called.
    class TestArrayList<E> extends ArrayList<E> {
      boolean toArrayCalled = false;

      @Override
      public Object[] toArray() {

   * this graph.
   *
   * <p>This is equal to the union of {@link #predecessors(Object)} and {@link #successors(Object)}.
   *
   * <p>If {@code node} is removed from the graph after this method is called, the {@code Set}
   * {@code view} returned by this method will be invalidated, and will throw {@code
   * IllegalStateException} if it is accessed in any way, with the following exceptions:
   *
   * <ul>

    * There is a **solution** to this, however.
* There's an **extension** to the **TLS** protocol (the one handling the encryption at the TCP level, before HTTP) called **<a href="https://en.wikipedia.org/wiki/Server_Name_Indication" class="external-link" target="_blank"><abbr title="Server Name Indication">SNI</abbr></a>**.

 * family. <b>Avoid</b> creating a mock or stub {@code Future}. Mock and stub implementations are
 * fragile because they assume that only certain methods will be called and because they often
 * implement subtleties of the API improperly.
 *
 * <p><b>Custom implementation</b>: Avoid implementing {@code ListenableFuture} from scratch. If you

 * resulting in notification could have occurred to an entry being manually removed or replaced, or
 * due to eviction resulting from timed expiration, exceeding a maximum size, or garbage collection.
 *
 * <p>An instance may be called concurrently by multiple threads to process different entries.
 * Implementations of this interface should avoid performing blocking calls or synchronizing on
 * shared resources.
 *

        String::class.java,
        String::class.java,
      )
    } catch (_: NoSuchMethodException) {
      null
    }

  /** Android method to clean and sort certificates, called via reflection. */
  @Suppress("unused", "UNCHECKED_CAST")
  fun checkServerTrusted(
    chain: Array<out X509Certificate>,
    authType: String,
    host: String,
  ): List<Certificate> {

  }

  /**
   * Returns an iterable whose iterator returns the given elements in order. The elements are copied
   * out of the source collection at the time this method is called.
   */
  @SuppressWarnings("unchecked") // Es come in, Es go out
  public static <E extends @Nullable Object> MinimalIterable<E> from(Collection<E> elements) {
    return (MinimalIterable) of(elements.toArray());
  }

### Technical Details: `root_path`

When you mount a sub-application as described above, FastAPI will take care of communicating the mount path for the sub-application using a mechanism from the ASGI specification called a `root_path`.

That way, the sub-application will know to use that path prefix for the docs UI.