Index: lib/Analysis/InstructionSimplify.cpp
===================================================================
--- lib/Analysis/InstructionSimplify.cpp
+++ lib/Analysis/InstructionSimplify.cpp
@@ -2128,6 +2128,41 @@
   return nullptr;
 }
 
+/// Return true if B is known to be implied by A.  A & B must be i1 (boolean)
+/// values. Note that the truth table for implication is the same as <=u on i1
+/// values (but not <=s!).  The truth table for both is:
+///    | T | F (B)
+///  T | T | F
+///  F | T | T
+/// (A)
+static bool implies(Value *A, Value *B) {
+  // TODO: Consider extending this to vector of i1?
+  assert(A->getType()->isIntegerTy(1) && B->getType()->isIntegerTy(1));
+  
+  // A ==> A by definition
+  if (A == B) return true;
+
+  // i +_{nsw} C_{>0} <s L ==> i <s L
+  auto *ICmpA = dyn_cast<ICmpInst>(A);
+  auto *ICmpB = dyn_cast<ICmpInst>(B);
+  if (!ICmpA || !ICmpB ||
+      ICmpA->getPredicate() != ICmpInst::ICMP_SLT ||
+      ICmpB->getPredicate() != ICmpInst::ICMP_SLT ||
+      ICmpA->getOperand(1) != ICmpB->getOperand(1))
+    return false;
+
+  auto *BO = dyn_cast<OverflowingBinaryOperator>(ICmpA->getOperand(0));
+  if (!BO || !BO->hasNoSignedWrap() ||
+      BO->getOperand(0) != ICmpB->getOperand(0))
+    return false;
+
+  ConstantInt *C = dyn_cast<ConstantInt>(BO->getOperand(1));
+  if (!C || C->isNegative())
+    return false;
+  
+  return true;    
+}
+
 /// SimplifyICmpInst - Given operands for an ICmpInst, see if we can
 /// fold the result.  If not, this returns null.
 static Value *SimplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
@@ -2176,6 +2211,8 @@
       // X >=u 1 -> X
       if (match(RHS, m_One()))
         return LHS;
+      if (implies(RHS, LHS))
+        return getTrue(ITy);
       break;
     case ICmpInst::ICMP_SLT:
       // X <s 0 -> X
@@ -2187,6 +2224,10 @@
       if (match(RHS, m_One()))
         return LHS;
       break;
+    case ICmpInst::ICMP_ULE:
+      if (implies(LHS, RHS))
+        return getTrue(ITy);
+      break;
     }
   }
 
Index: test/Transforms/InstSimplify/implies.ll
===================================================================
--- test/Transforms/InstSimplify/implies.ll
+++ test/Transforms/InstSimplify/implies.ll
@@ -0,0 +1,55 @@
+; RUN: opt -S %s -instsimplify | FileCheck %s
+
+; A ==> A -> true
+define i1 @test(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test
+; CHECK: ret i1 true
+  %var29 = icmp slt i32 %i, %length.i
+  %res = icmp uge i1 %var29, %var29
+  ret i1 %res
+}
+
+; i +_{nsw} C_{>0} <s L ==> i <s L -> true
+define i1 @test2(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test2
+; CHECK: ret i1 true
+  %iplus1 = add nsw i32 %i, 1
+  %var29 = icmp slt i32 %i, %length.i
+  %var30 = icmp slt i32 %iplus1, %length.i
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; i + C_{>0} <s L ==> i <s L -> unknown without the nsw
+define i1 @test2_neg(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test2_neg
+; CHECK:   ret i1 %res
+  %iplus1 = add i32 %i, 1
+  %var29 = icmp slt i32 %i, %length.i
+  %var30 = icmp slt i32 %iplus1, %length.i
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; sle is not implication
+define i1 @test2_neg2(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test2_neg2
+; CHECK:   ret i1 %res
+  %iplus1 = add i32 %i, 1
+  %var29 = icmp slt i32 %i, %length.i
+  %var30 = icmp slt i32 %iplus1, %length.i
+  %res = icmp sle i1 %var30, %var29
+  ret i1 %res
+}
+
+; i +_{nsw} C_{>0} <s L ==> i <s L -> true
+; With an inverted conditional (ule B A rather than canonical ugt A B
+define i1 @test3(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test3
+; CHECK: ret i1 true
+  %iplus1 = add nsw i32 %i, 1
+  %var29 = icmp slt i32 %i, %length.i
+  %var30 = icmp slt i32 %iplus1, %length.i
+  %res = icmp uge i1 %var29, %var30
+  ret i1 %res
+}