[3.13] gh-120361: Add `nonmember` test with enum flags inside to `test_enum` (GH-120364) (#120511)

gh-120361: Add `nonmember` test with enum flags inside to `test_enum` (GH-120364)

* gh-120361: Add `nonmember` test with enum flags inside to `test_enum`
(cherry picked from commit 7fadfd82eb)

Co-authored-by: Nikita Sobolev <mail@sobolevn.me>

Doc/library/enum.rst

@@ -527,7 +527,7 @@ Data Types
 
    ``Flag`` is the same as :class:`Enum`, but its members support the bitwise
    operators ``&`` (*AND*), ``|`` (*OR*), ``^`` (*XOR*), and ``~`` (*INVERT*);
-   the results of those operators are members of the enumeration.
+   the results of those operations are (aliases of) members of the enumeration.
 
    .. method:: __contains__(self, value)
 

Lib/test/test_enum.py

@@ -1495,6 +1495,27 @@ class TestSpecial(unittest.TestCase):
             spam = nonmember(SpamEnumIsInner)
         self.assertTrue(SpamEnum.spam is SpamEnumIsInner)
 
+    def test_using_members_as_nonmember(self):
+        class Example(Flag):
+            A = 1
+            B = 2
+            ALL = nonmember(A | B)
+
+        self.assertEqual(Example.A.value, 1)
+        self.assertEqual(Example.B.value, 2)
+        self.assertEqual(Example.ALL, 3)
+        self.assertIs(type(Example.ALL), int)
+
+        class Example(Flag):
+            A = auto()
+            B = auto()
+            ALL = nonmember(A | B)
+
+        self.assertEqual(Example.A.value, 1)
+        self.assertEqual(Example.B.value, 2)
+        self.assertEqual(Example.ALL, 3)
+        self.assertIs(type(Example.ALL), int)
+
     def test_nested_classes_in_enum_with_member(self):
         """Support locally-defined nested classes."""
         class Outer(Enum):