Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -7005,6 +7005,24 @@
   WalkingBEDominatingConds = true;
   ClearWalkingBEDominatingCondsOnExit ClearOnExit(*this);
 
+  // See if we can exploit an already computed trip count to prove the
+  // predicate.
+  auto BECountIt = BackedgeTakenCounts.find(L);
+  if (BECountIt != BackedgeTakenCounts.end()) {
+    const SCEV *LatchBECount = BECountIt->second.getExact(Latch, this);
+    if (LatchBECount != getCouldNotCompute()) {
+      // We know that Latch branches back to the loop header exactly
+      // LatchBECount times.  This means the backdege condition at Latch is
+      // equivalent to  "{0,+,1} u< LatchBECount".
+      Type *Ty = LatchBECount->getType();
+      const SCEV *LoopCounter =
+          getAddRecExpr(getZero(Ty), getOne(Ty), L, SCEV::FlagAnyWrap);
+      if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
+                        LatchBECount))
+        return true;
+    }
+  }
+
   // Check conditions due to any @llvm.assume intrinsics.
   for (auto &AssumeVH : AC.assumptions()) {
     if (!AssumeVH)
Index: test/Transforms/IndVarSimplify/eliminate-comparison.ll
===================================================================
--- test/Transforms/IndVarSimplify/eliminate-comparison.ll
+++ test/Transforms/IndVarSimplify/eliminate-comparison.ll
@@ -292,5 +292,42 @@
   ret void
 }
 
-!0 = !{i32 0, i32 2147483647}
+define i1 @func_16(i16* %tmp20, i32* %len.addr) {
+; CHECK-LABEL: @func_16(
+entry:
+  %len = load i32, i32* %len.addr, !range !0
+  %tmp18 = icmp eq i32 %len, 0
+  br i1 %tmp18, label %bb2, label %bb0.preheader
+
+bb0.preheader:
+  br label %bb0
+
+bb0:
+; CHECK: bb0:
+  %var_0.in = phi i32 [ %var_0, %bb1 ], [ %len, %bb0.preheader ]
+  %var_1 = phi i32 [ %tmp30, %bb1 ], [ 0, %bb0.preheader ]
+  %var_0 = add nsw i32 %var_0.in, -1
+  %tmp23 = icmp ult i32 %var_1, %len
+; CHECK: br i1 true, label %stay, label %bb2.loopexit
+  br i1 %tmp23, label %stay, label %bb2
+
+stay:
+; CHECK: stay:
+  %tmp25 = getelementptr inbounds i16, i16* %tmp20, i32 %var_1
+  %tmp26 = load i16, i16* %tmp25
+  %tmp29 = icmp eq i16 %tmp26, 0
+  br i1 %tmp29, label %bb1, label %bb2
+
+bb1:
+  %tmp30 = add i32 %var_1, 1
+  %tmp31 = icmp eq i32 %var_0, 0
+  br i1 %tmp31, label %bb3, label %bb0
+
+bb2:
+  ret i1 false
+
+bb3:
+  ret i1 true
+}
 
+!0 = !{i32 0, i32 2147483647}