diff --git a/mlir/include/mlir/Dialect/Linalg/Transforms/ComprehensiveBufferize.h b/mlir/include/mlir/Dialect/Linalg/Transforms/ComprehensiveBufferize.h
--- a/mlir/include/mlir/Dialect/Linalg/Transforms/ComprehensiveBufferize.h
+++ b/mlir/include/mlir/Dialect/Linalg/Transforms/ComprehensiveBufferize.h
@@ -139,23 +139,8 @@
   void dumpEquivalences() const;
 
 private:
-  /// llvm::EquivalenceClasses wants comparable elements because it uses
-  /// std::set as the underlying impl.
-  /// ValueWrapper wraps Value and uses pointer comparison on the defining op.
-  /// This is a poor man's comparison but it's not like UnionFind needs ordering
-  /// anyway ..
-  struct ValueWrapper {
-    ValueWrapper(Value val) : v(val) {}
-    operator Value() const { return v; }
-    bool operator<(const ValueWrapper &wrap) const {
-      return v.getImpl() < wrap.v.getImpl();
-    }
-    bool operator==(const ValueWrapper &wrap) const { return v == wrap.v; }
-    Value v;
-  };
-
-  using EquivalenceClassRangeType = llvm::iterator_range<
-      llvm::EquivalenceClasses<ValueWrapper>::member_iterator>;
+  using EquivalenceClassRangeType =
+      llvm::iterator_range<llvm::EquivalenceClasses<Value>::member_iterator>;
   /// Check that aliasInfo for `v` exists and return a reference to it.
   EquivalenceClassRangeType getAliases(Value v) const;
 
@@ -222,10 +207,10 @@
   /// Auxiliary structure to store all the values a given value aliases with.
   /// These are the conservative cases that can further decompose into
   /// "equivalent" buffer relationships.
-  llvm::EquivalenceClasses<ValueWrapper> aliasInfo;
+  llvm::EquivalenceClasses<Value> aliasInfo;
 
   /// Auxiliary structure to store all the equivalent buffer classes.
-  llvm::EquivalenceClasses<ValueWrapper> equivalentInfo;
+  llvm::EquivalenceClasses<Value> equivalentInfo;
 };
 
 /// Analyze the `ops` to determine which OpResults are inplaceable:
diff --git a/mlir/include/mlir/IR/Value.h b/mlir/include/mlir/IR/Value.h
--- a/mlir/include/mlir/IR/Value.h
+++ b/mlir/include/mlir/IR/Value.h
@@ -114,6 +114,7 @@
   explicit operator bool() const { return impl; }
   bool operator==(const Value &other) const { return impl == other.impl; }
   bool operator!=(const Value &other) const { return !(*this == other); }
+  bool operator<(const Value &other) const { return impl < other.impl; }
 
   /// Return the type of this value.
   Type getType() const { return impl->getType(); }
diff --git a/mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp b/mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/ComprehensiveBufferize.cpp
@@ -976,11 +976,11 @@
   for (auto mit = leaderIt, meit = equivalentInfo.member_end(); mit != meit;
        ++mit) {
     auto extractSliceOp =
-        dyn_cast_or_null<ExtractSliceOp>(mit->v.getDefiningOp());
+        dyn_cast_or_null<ExtractSliceOp>(mit->getDefiningOp());
     if (extractSliceOp &&
         areEquivalentExtractSliceOps(extractSliceOp, insertSliceOp) &&
         getInPlace(extractSliceOp.result()) == InPlaceSpec::True) {
-      LDBG("\tfound: " << *mit->v.getDefiningOp() << '\n');
+      LDBG("\tfound: " << *mit->getDefiningOp() << '\n');
       return true;
     }
   }
@@ -994,7 +994,7 @@
   auto leaderIt = equivalentInfo.findLeader(v);
   for (auto mit = leaderIt, meit = equivalentInfo.member_end(); mit != meit;
        ++mit) {
-    fun(mit->v);
+    fun(*mit);
   }
 }
 
@@ -1091,10 +1091,10 @@
     auto leaderIt = equivalentInfo.findLeader(valueToClobber);
     for (auto mit = leaderIt, meit = equivalentInfo.member_end(); mit != meit;
          ++mit) {
-      Operation *candidateOp = mit->v.getDefiningOp();
+      Operation *candidateOp = mit->getDefiningOp();
       if (!candidateOp)
         continue;
-      auto maybeAliasingOperand = getAliasingOpOperand(mit->v.cast<OpResult>());
+      auto maybeAliasingOperand = getAliasingOpOperand(mit->cast<OpResult>());
       if (!maybeAliasingOperand || !*maybeAliasingOperand ||
           !bufferizesToMemoryWrite(**maybeAliasingOperand))
         continue;