diff --git a/llvm/include/llvm/Analysis/ConstraintSystem.h b/llvm/include/llvm/Analysis/ConstraintSystem.h
--- a/llvm/include/llvm/Analysis/ConstraintSystem.h
+++ b/llvm/include/llvm/Analysis/ConstraintSystem.h
@@ -46,6 +46,17 @@
 
   /// Retuns true if there may be a solution for the constraints in the system.
   bool mayHaveSolution();
+
+  static SmallVector<int64_t, 8> negate(SmallVector<int64_t, 8> R) {
+    // The negated constraint R is obtained by multiplying by -1 and adding 1 to
+    // the constant.
+    R[0] += 1;
+    for (unsigned i = 0; i < R.size(); i++)
+      R[i] *= -1;
+    return R;
+  }
+
+  bool isConditionImplied(SmallVector<int64_t, 8> R);
 };
 } // namespace llvm
 
diff --git a/llvm/lib/Analysis/ConstraintSystem.cpp b/llvm/lib/Analysis/ConstraintSystem.cpp
--- a/llvm/lib/Analysis/ConstraintSystem.cpp
+++ b/llvm/lib/Analysis/ConstraintSystem.cpp
@@ -109,3 +109,13 @@
     std::cout << "\n";
   }
 }
+
+bool ConstraintSystem::isConditionImplied(SmallVector<int64_t, 8> R) {
+  // If there is no solution with the negation of R added to the system, the
+  // condition must hold based on the exsisting constraints.
+  R = ConstraintSystem::negate(R);
+
+  auto NewSystem = *this;
+  NewSystem.addVariableRow(R);
+  return !NewSystem.mayHaveSolution();
+}
diff --git a/llvm/unittests/Analysis/ConstraintSystemTest.cpp b/llvm/unittests/Analysis/ConstraintSystemTest.cpp
--- a/llvm/unittests/Analysis/ConstraintSystemTest.cpp
+++ b/llvm/unittests/Analysis/ConstraintSystemTest.cpp
@@ -79,4 +79,68 @@
     EXPECT_TRUE(CS.mayHaveSolution());
   }
 }
+
+TEST(ConstraintSloverTest, IsConditionImplied) {
+  {
+    // For the test below, we assume we know
+    // x <= 5 && y <= 3
+    ConstraintSystem CS;
+    CS.addVariableRow({5, 1, 0});
+    CS.addVariableRow({3, 0, 1});
+
+    // x + y <= 6 does not hold.
+    EXPECT_FALSE(CS.isConditionImplied({6, 1, 1}));
+    // x + y <= 7 does not hold.
+    EXPECT_FALSE(CS.isConditionImplied({7, 1, 1}));
+    // x + y <= 8 does hold.
+    EXPECT_TRUE(CS.isConditionImplied({8, 1, 1}));
+
+    // 2 * x + y <= 12 does hold.
+    EXPECT_FALSE(CS.isConditionImplied({12, 2, 1}));
+    // 2 * x + y <= 13 does hold.
+    EXPECT_TRUE(CS.isConditionImplied({13, 2, 1}));
+
+    //  x + y <= 12 does hold.
+    EXPECT_FALSE(CS.isConditionImplied({12, 2, 1}));
+    // 2 * x + y <= 13 does hold.
+    EXPECT_TRUE(CS.isConditionImplied({13, 2, 1}));
+
+    // x <= y == x - y <= 0 does not hold.
+    EXPECT_FALSE(CS.isConditionImplied({0, 1, -1}));
+    // y <= x == -x + y <= 0 does not hold.
+    EXPECT_FALSE(CS.isConditionImplied({0, -1, 1}));
+  }
+
+  {
+    // For the test below, we assume we know
+    // x + 1 <= y + 1 == x - y <= 0
+    ConstraintSystem CS;
+    CS.addVariableRow({0, 1, -1});
+
+    // x <= y == x - y <= 0 does hold.
+    EXPECT_TRUE(CS.isConditionImplied({0, 1, -1}));
+    // y <= x == -x + y <= 0 does not hold.
+    EXPECT_FALSE(CS.isConditionImplied({0, -1, 1}));
+
+    // x <= y + 10 == x - y <= 10 does hold.
+    EXPECT_TRUE(CS.isConditionImplied({10, 1, -1}));
+    // x + 10 <= y == x - y <= -10 does NOT hold.
+    EXPECT_FALSE(CS.isConditionImplied({-10, 1, -1}));
+  }
+
+  {
+    // For the test below, we assume we know
+    // x <= y == x - y <= 0
+    // y <= z == y - x <= 0
+    ConstraintSystem CS;
+    CS.addVariableRow({0, 1, -1, 0});
+    CS.addVariableRow({0, 0, 1, -1});
+
+    // z <= y == -y + z <= 0 does not hold.
+    EXPECT_FALSE(CS.isConditionImplied({0, 0, -1, 1}));
+    // x <= z == x - z <= 0 does hold.
+    EXPECT_TRUE(CS.isConditionImplied({0, 1, 0, -1}));
+  }
+}
+
 } // namespace