Index: llvm/lib/Analysis/ValueTracking.cpp
===================================================================
--- llvm/lib/Analysis/ValueTracking.cpp
+++ llvm/lib/Analysis/ValueTracking.cpp
@@ -7938,6 +7938,10 @@
     // LHS u<= LHS +_{nuw} C   for any C
     if (match(RHS, m_NUWAdd(m_Specific(LHS), m_APInt(C))))
       return true;
+    
+    // (RHS >> X) u<= RHS      for any X
+    if (match(LHS, m_LShr(m_Specific(RHS), m_Value())))
+      return true;
 
     // Match A to (X +_{nuw} CA) and B to (X +_{nuw} CB)
     auto MatchNUWAddsToSameValue = [&](const Value *A, const Value *B,
@@ -7993,6 +7997,13 @@
         isTruePredicate(CmpInst::ICMP_ULE, ARHS, BRHS, DL, Depth))
       return true;
     return std::nullopt;
+  
+  case CmpInst::ICMP_UGT:
+  case CmpInst::ICMP_UGE:
+      if (isTruePredicate(CmpInst::ICMP_ULE, ALHS, BLHS, DL, Depth) &&
+        isTruePredicate(CmpInst::ICMP_ULE, BRHS, ARHS, DL, Depth))
+      return true;
+    return std::nullopt;  
   }
 }