diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index 6bc7b2b..a713314 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -361,6 +361,8 @@
                 self.value = value
             def __lt__(self, other):
                 return self.value < other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -375,6 +377,8 @@
                 self.value = value
             def __le__(self, other):
                 return self.value <= other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -389,6 +393,8 @@
                 self.value = value
             def __gt__(self, other):
                 return self.value > other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -403,6 +409,8 @@
                 self.value = value
             def __ge__(self, other):
                 return self.value >= other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -428,6 +436,22 @@
             class A:
                 pass
 
+    def test_bug_10042(self):
+        @functools.total_ordering
+        class TestTO:
+            def __init__(self, value):
+                self.value = value
+            def __eq__(self, other):
+                if isinstance(other, TestTO):
+                    return self.value == other.value
+                return False
+            def __lt__(self, other):
+                if isinstance(other, TestTO):
+                    return self.value < other.value
+                raise TypeError
+        with self.assertRaises(TypeError):
+            TestTO(8) <= ()
+
 def test_main(verbose=None):
     test_classes = (
         TestPartial,