RangeMap<Integer, Integer> sub1 = rangeMap.subRangeMap(Range.closed(5, 11));
    assertEquals(
        ImmutableMap.of(Range.closedOpen(5, 7), 1, Range.closed(9, 10), 2), sub1.asMapOfRanges());
    RangeMap<Integer, Integer> sub2 = sub1.subRangeMap(Range.open(6, 15));
    assertEquals(
        ImmutableMap.of(Range.open(6, 7), 1, Range.closed(9, 10), 2), sub2.asMapOfRanges());
  }

# Sub-dependencies

You can create dependencies that have **sub-dependencies**.

They can be as **deep** as you need them to be.

**FastAPI** will take care of solving them.

## First dependency "dependable"

You could create a first dependency ("dependable") like:

//// tab | Python 3.10+

```Python hl_lines="8-9"
{!> ../../docs_src/dependencies/tutorial005_an_py310.py!}
```

////

//// tab | Python 3.9+

### Aplicação de nível superior

Primeiro, crie a aplicação principal, de nível superior, **FastAPI**, e suas *operações de rota*:

```Python hl_lines="3  6-8"
{!../../docs_src/sub_applications/tutorial001.py!}
```

### Sub-aplicação

Em seguida, crie sua sub-aplicação e suas *operações de rota*.

Essa sub-aplicação é apenas outra aplicação FastAPI padrão, mas esta é a que será "montada":

### 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.

下图显示的是主应用 API 文档，只包括其自有的*路径操作*。

<img src="/img/tutorial/sub-applications/image01.png">

然后查看子应用文档 <a href="http://127.0.0.1:8000/subapi/docs" class="external-link" target="_blank">http://127.0.0.1:8000/subapi/docs。</a>

下图显示的是子应用的 API 文档，也是只包括其自有的*路径操作*，所有这些路径操作都在 `/subapi` 子路径前缀下。

<img src="/img/tutorial/sub-applications/image02.png">

两个用户界面都可以正常运行，因为浏览器能够与每个指定的应用或子应用会话。

### 技术细节：`root_path`

Sie sehen die automatische API-Dokumentation für die Hauptanwendung, welche nur deren eigene _Pfadoperationen_ anzeigt:

<img src="/img/tutorial/sub-applications/image01.png">

Öffnen Sie dann die Dokumentation für die Unteranwendung unter <a href="http://127.0.0.1:8000/subapi/docs" class="external-link" target="_blank">http://127.0.0.1:8000/subapi/docs</a>.

👆 🔜 👀 🏧 🛠️ 🩺 👑 📱, 🔌 🕴 🚮 👍 _➡ 🛠️_:

<img src="/img/tutorial/sub-applications/image01.png">

&amp; ⤴️, 📂 🩺 🎧-🈸, <a href="http://127.0.0.1:8000/subapi/docs" class="external-link" target="_blank">http://127.0.0.1:8000/subapi/docs</a>.

👆 🔜 👀 🏧 🛠️ 🩺 🎧-🈸, ✅ 🕴 🚮 👍 _➡ 🛠️_, 🌐 🔽 ☑ 🎧-➡ 🔡 `/subapi`:

<img src="/img/tutorial/sub-applications/image02.png">

	ADDE	R1, R2                // b9880021
	SUB	R3, R4                // b9090043
	SUB	R3, R4, R5            // b9e93054
	SUB	$8192, R3             // a73be000
	SUB	$8192, R3, R4         // ec43e00000d9
	SUBC	R1, R2                // b90b0021
	SUBC	$1, R1, R2            // ec21ffff00db
	SUBC	R2, R3, R4            // b9eb2043
	SUBW	R3, R4                // 1b43
	SUBW	R3, R4, R5            // b9f93054

TEXT	foo(SB), DUPOK|NOSPLIT, $0

	ADDF	F0, F1, F2    // 002a31ee
	ADDD.EQ	F3, F4, F5    // 035b340e
	ADDF.NE	F0, F2        // 002a321e
	ADDD	F3, F5        // 035b35ee
	SUBF	F0, F1, F2    // 402a31ee
	SUBD.EQ	F3, F4, F5    // 435b340e
	SUBF.NE	F0, F2        // 402a321e
	SUBD	F3, F5        // 435b35ee
	MULF	F0, F1, F2    // 002a21ee
	MULD.EQ	F3, F4, F5    // 035b240e
	MULF.NE	F0, F2        // 002a221e
	MULD	F3, F5        // 035b25ee

	SUBMEVCC R3, R4                 // 7c8305d1
	SUBV R3, R4, R5                 // 7ca32450
	SUBE R3, R4, R5                 // 7ca32110
	SUBECC R3, R4, R5               // 7ca32111
	SUBEV R3, R4, R5                // 7ca32510
	SUBEVCC R3, R4, R5              // 7ca32511
	SUBC R3, $65536, R4             // 3fe00001600000007c83f810
	SUBC R3, $65537, R4             // 3fe0000163ff00017c83f810