diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -8024,12 +8024,17 @@
   }
 
   case CmpInst::ICMP_ULE: {
+    const Value *V;
     const APInt *C;
 
     // LHS u<= LHS +_{nuw} C   for any C
     if (match(RHS, m_NUWAdd(m_Specific(LHS), m_APInt(C))))
       return true;
 
+    // RHS >> V u<= RHS for any V
+    if (match(LHS, m_LShr(m_Specific(RHS), m_Value(V))))
+      return true;
+
     // Match A to (X +_{nuw} CA) and B to (X +_{nuw} CB)
     auto MatchNUWAddsToSameValue = [&](const Value *A, const Value *B,
                                        const Value *&X,
diff --git a/llvm/test/Transforms/InstSimplify/implies.ll b/llvm/test/Transforms/InstSimplify/implies.ll
--- a/llvm/test/Transforms/InstSimplify/implies.ll
+++ b/llvm/test/Transforms/InstSimplify/implies.ll
@@ -449,9 +449,8 @@
 ; CHECK-LABEL: @test_shift(
 ; CHECK-NEXT:    [[LSHR:%.*]] = lshr i64 [[X:%.*]], [[SHIFT:%.*]]
 ; CHECK-NEXT:    [[ICMP1:%.*]] = icmp ugt i64 [[LSHR]], [[Y:%.*]]
-; CHECK-NEXT:    [[ICMP2:%.*]] = icmp ugt i64 [[X]], [[Y]]
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[ICMP1]])
-; CHECK-NEXT:    ret i1 [[ICMP2]]
+; CHECK-NEXT:    ret i1 true
 ;
   %lshr = lshr i64 %x, %shift
   %icmp1 = icmp ugt i64 %lshr, %y
@@ -479,11 +478,7 @@
 ; i <u L ==> i >> C <u L
 define i1 @lshr_constant(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @lshr_constant(
-; CHECK-NEXT:    [[SHL:%.*]] = lshr i32 [[I:%.*]], 1
-; CHECK-NEXT:    [[VAR29:%.*]] = icmp ult i32 [[I]], [[LENGTH_I:%.*]]
-; CHECK-NEXT:    [[VAR30:%.*]] = icmp ult i32 [[SHL]], [[LENGTH_I]]
-; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR29]], [[VAR30]]
-; CHECK-NEXT:    ret i1 [[RES]]
+; CHECK-NEXT:    ret i1 true
 ;
   %shl = lshr i32 %i, 1
   %var29 = icmp ult i32 %i, %length.i
@@ -495,11 +490,7 @@
 ; i <u L ==> i >> V <u L
 define i1 @lshr_value(i32 %length.i, i32 %i, i32 %v) {
 ; CHECK-LABEL: @lshr_value(
-; CHECK-NEXT:    [[SHL:%.*]] = lshr i32 [[I:%.*]], [[V:%.*]]
-; CHECK-NEXT:    [[VAR29:%.*]] = icmp ult i32 [[I]], [[LENGTH_I:%.*]]
-; CHECK-NEXT:    [[VAR30:%.*]] = icmp ult i32 [[SHL]], [[LENGTH_I]]
-; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR29]], [[VAR30]]
-; CHECK-NEXT:    ret i1 [[RES]]
+; CHECK-NEXT:    ret i1 true
 ;
   %shl = lshr i32 %i, %v
   %var29 = icmp ult i32 %i, %length.i