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
@@ -1,10 +1,10 @@
-; NOTE: Assertions have been autogenerated by update_test_checks.py
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
 ; RUN: opt -S %s -passes=instsimplify | FileCheck %s
 
 ; A ==> A -> true
 define i1 @test(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %var29 = icmp slt i32 %i, %length.i
   %res = icmp uge i1 %var29, %var29
@@ -14,7 +14,7 @@
 ; 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
+; CHECK-NEXT:    ret i1 true
 ;
   %iplus1 = add nsw i32 %i, 1
   %var29 = icmp slt i32 %i, %length.i
@@ -26,9 +26,9 @@
 ; 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:         [[IPLUS1:%.*]] = add i32 %i, 1
-; CHECK-NEXT:    [[VAR29:%.*]] = icmp slt i32 %i, %length.i
-; CHECK-NEXT:    [[VAR30:%.*]] = icmp slt i32 [[IPLUS1]], %length.i
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp slt i32 [[I]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp slt i32 [[IPLUS1]], [[LENGTH_I]]
 ; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
 ; CHECK-NEXT:    ret i1 [[RES]]
 ;
@@ -42,9 +42,9 @@
 ; sle is not implication
 define i1 @test2_neg2(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test2_neg2(
-; CHECK:         [[IPLUS1:%.*]] = add i32 %i, 1
-; CHECK-NEXT:    [[VAR29:%.*]] = icmp slt i32 %i, %length.i
-; CHECK-NEXT:    [[VAR30:%.*]] = icmp slt i32 [[IPLUS1]], %length.i
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp slt i32 [[I]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp slt i32 [[IPLUS1]], [[LENGTH_I]]
 ; CHECK-NEXT:    [[RES:%.*]] = icmp sle i1 [[VAR30]], [[VAR29]]
 ; CHECK-NEXT:    ret i1 [[RES]]
 ;
@@ -58,9 +58,9 @@
 ; The binary operator has to be an add
 define i1 @test2_neg3(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test2_neg3(
-; CHECK:         [[IPLUS1:%.*]] = sub nsw i32 %i, 1
-; CHECK-NEXT:    [[VAR29:%.*]] = icmp slt i32 %i, %length.i
-; CHECK-NEXT:    [[VAR30:%.*]] = icmp slt i32 [[IPLUS1]], %length.i
+; CHECK-NEXT:    [[IPLUS1:%.*]] = sub nsw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp slt i32 [[I]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp slt i32 [[IPLUS1]], [[LENGTH_I]]
 ; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
 ; CHECK-NEXT:    ret i1 [[RES]]
 ;
@@ -75,7 +75,7 @@
 ; 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
+; CHECK-NEXT:    ret i1 true
 ;
   %iplus1 = add nsw i32 %i, 1
   %var29 = icmp slt i32 %i, %length.i
@@ -87,7 +87,7 @@
 ; i +_{nuw} C <u L ==> i <u L
 define i1 @test4(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test4(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %iplus1 = add nuw i32 %i, 1
   %var29 = icmp ult i32 %i, %length.i
@@ -99,7 +99,7 @@
 ; A ==> A for vectors
 define <4 x i1> @test5(<4 x i1> %vec) {
 ; CHECK-LABEL: @test5(
-; CHECK:         ret <4 x i1> <i1 true, i1 true, i1 true, i1 true>
+; CHECK-NEXT:    ret <4 x i1> <i1 true, i1 true, i1 true, i1 true>
 ;
   %res = icmp ule <4 x i1> %vec, %vec
   ret <4 x i1> %res
@@ -108,7 +108,7 @@
 ; Don't crash on vector inputs - pr25040
 define <4 x i1> @test6(<4 x i1> %a, <4 x i1> %b) {
 ; CHECK-LABEL: @test6(
-; CHECK:         [[RES:%.*]] = icmp ule <4 x i1> %a, %b
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule <4 x i1> [[A:%.*]], [[B:%.*]]
 ; CHECK-NEXT:    ret <4 x i1> [[RES]]
 ;
   %res = icmp ule <4 x i1> %a, %b
@@ -118,7 +118,7 @@
 ; i +_{nsw} 1 <s L  ==> i < L +_{nsw} 1
 define i1 @test7(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test7(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %iplus1 = add nsw i32 %i, 1
   %len.plus.one = add nsw i32 %length.i, 1
@@ -131,7 +131,7 @@
 ; i +_{nuw} 1 <u L  ==> i < L +_{nuw} 1
 define i1 @test8(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test8(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %iplus1 = add nuw i32 %i, 1
   %len.plus.one = add nuw i32 %length.i, 1
@@ -144,7 +144,7 @@
 ; i +_{nuw} C <u L ==> i < L, even if C is negative
 define i1 @test9(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test9(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %iplus1 = add nuw i32 %i, -100
   %var29 = icmp ult i32 %i, %length.i
@@ -155,7 +155,7 @@
 
 define i1 @test10(i32 %length.i, i32 %x.full) {
 ; CHECK-LABEL: @test10(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %x = and i32 %x.full, 4294901760  ;; 4294901760 == 0xffff0000
   %large = or i32 %x, 100
@@ -168,10 +168,10 @@
 
 define i1 @test11(i32 %length.i, i32 %x) {
 ; CHECK-LABEL: @test11(
-; CHECK:         [[LARGE:%.*]] = or i32 %x, 100
-; CHECK-NEXT:    [[SMALL:%.*]] = or i32 %x, 90
-; CHECK-NEXT:    [[KNOWN:%.*]] = icmp ult i32 [[LARGE]], %length.i
-; CHECK-NEXT:    [[TO_PROVE:%.*]] = icmp ult i32 [[SMALL]], %length.i
+; CHECK-NEXT:    [[LARGE:%.*]] = or i32 [[X:%.*]], 100
+; CHECK-NEXT:    [[SMALL:%.*]] = or i32 [[X]], 90
+; CHECK-NEXT:    [[KNOWN:%.*]] = icmp ult i32 [[LARGE]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[TO_PROVE:%.*]] = icmp ult i32 [[SMALL]], [[LENGTH_I]]
 ; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[KNOWN]], [[TO_PROVE]]
 ; CHECK-NEXT:    ret i1 [[RES]]
 ;
@@ -185,11 +185,11 @@
 
 define i1 @test12(i32 %length.i, i32 %x.full) {
 ; CHECK-LABEL: @test12(
-; CHECK:         [[X:%.*]] = and i32 [[X:%.*]].full, -65536
+; CHECK-NEXT:    [[X:%.*]] = and i32 [[X_FULL:%.*]], -65536
 ; CHECK-NEXT:    [[LARGE:%.*]] = or i32 [[X]], 65536
 ; CHECK-NEXT:    [[SMALL:%.*]] = or i32 [[X]], 90
-; CHECK-NEXT:    [[KNOWN:%.*]] = icmp ult i32 [[LARGE]], %length.i
-; CHECK-NEXT:    [[TO_PROVE:%.*]] = icmp ult i32 [[SMALL]], %length.i
+; CHECK-NEXT:    [[KNOWN:%.*]] = icmp ult i32 [[LARGE]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[TO_PROVE:%.*]] = icmp ult i32 [[SMALL]], [[LENGTH_I]]
 ; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[KNOWN]], [[TO_PROVE]]
 ; CHECK-NEXT:    ret i1 [[RES]]
 ;
@@ -204,7 +204,7 @@
 
 define i1 @test13(i32 %length.i, i32 %x) {
 ; CHECK-LABEL: @test13(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %large = add nuw i32 %x, 100
   %small = add nuw i32 %x, 90
@@ -216,7 +216,7 @@
 
 define i1 @test14(i32 %length.i, i32 %x.full) {
 ; CHECK-LABEL: @test14(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %x = and i32 %x.full, 4294905615  ;; 4294905615 == 0xffff0f0f
   %large = or i32 %x, 8224 ;; == 0x2020
@@ -229,10 +229,10 @@
 
 define i1 @test15(i32 %length.i, i32 %x) {
 ; CHECK-LABEL: @test15(
-; CHECK:         [[LARGE:%.*]] = add nuw i32 %x, 100
-; CHECK-NEXT:    [[SMALL:%.*]] = add nuw i32 %x, 110
-; CHECK-NEXT:    [[KNOWN:%.*]] = icmp ult i32 [[LARGE]], %length.i
-; CHECK-NEXT:    [[TO_PROVE:%.*]] = icmp ult i32 [[SMALL]], %length.i
+; CHECK-NEXT:    [[LARGE:%.*]] = add nuw i32 [[X:%.*]], 100
+; CHECK-NEXT:    [[SMALL:%.*]] = add nuw i32 [[X]], 110
+; CHECK-NEXT:    [[KNOWN:%.*]] = icmp ult i32 [[LARGE]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[TO_PROVE:%.*]] = icmp ult i32 [[SMALL]], [[LENGTH_I]]
 ; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[KNOWN]], [[TO_PROVE]]
 ; CHECK-NEXT:    ret i1 [[RES]]
 ;
@@ -247,7 +247,7 @@
 ; X >=(s) Y == X ==> Y (i1 1 becomes -1 for reasoning)
 define i1 @test_sge(i32 %length.i, i32 %i) {
 ; CHECK-LABEL: @test_sge(
-; CHECK:         ret i1 true
+; CHECK-NEXT:    ret i1 true
 ;
   %iplus1 = add nsw nuw i32 %i, 1
   %var29 = icmp ult i32 %i, %length.i
@@ -267,3 +267,229 @@
   %res = icmp sle i1 %var29, %var30
   ret i1 %res
 }
+
+; X +_{nsw} 1 <(s) Y ==> X <(s) Y
+define i1 @test_sgt_icmp(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_sgt_icmp(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nsw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp sgt i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp sgt i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nsw i32 %i, 1
+  %var29 = icmp sgt i32 %length.i, %i
+  %var30 = icmp sgt i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; X +_{nsw} 1 <=(s) Y ==> X <=(s) Y
+define i1 @test_sge_icmp(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_sge_icmp(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nsw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp sge i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp sge i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nsw i32 %i, 1
+  %var29 = icmp sge i32 %length.i, %i
+  %var30 = icmp sge i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; X +_{nuw} 1 <(u) Y ==> X <(u) Y
+define i1 @test_ugt_icmp(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_ugt_icmp(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nuw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp ugt i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp ugt i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nuw i32 %i, 1
+  %var29 = icmp ugt i32 %length.i, %i
+  %var30 = icmp ugt i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; X +_{nuw} 1 <=(u) Y ==> X <=(u) Y
+define i1 @test_uge_icmp(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_uge_icmp(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nuw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp uge i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp uge i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nuw i32 %i, 1
+  %var29 = icmp uge i32 %length.i, %i
+  %var30 = icmp uge i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; negative case, X + 1 <(s) Y !==> X <(s) Y (X = 0x7fffffff, Y = 0x7fbfffff)
+define i1 @test_sgt_icmp_no_nsw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_sgt_icmp_no_nsw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp sgt i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp sgt i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add i32 %i, 1
+  %var29 = icmp sgt i32 %length.i, %i
+  %var30 = icmp sgt i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; negative case, X +_{nuw} 1 <(s) Y !==> X <(s) Y
+define i1 @test_sgt_icmp_nuw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_sgt_icmp_nuw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nuw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp sgt i32 [[I]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp sgt i32 [[IPLUS1]], [[LENGTH_I]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nuw i32 %i, 1
+  %var29 = icmp sgt i32 %i, %length.i
+  %var30 = icmp sgt i32 %iplus1, %length.i
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; negative case, X + 1 <=(s) Y !==> X <=(s) Y (X = 0x7fffffff, Y = 0x80000000)
+define i1 @test_sge_icmp_no_nsw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_sge_icmp_no_nsw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp sge i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp sge i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add i32 %i, 1
+  %var29 = icmp sge i32 %length.i, %i
+  %var30 = icmp sge i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; negative case, X +_{nuw} 1 <=(s) Y !==> X <=(s) Y
+define i1 @test_sge_icmp_nuw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_sge_icmp_nuw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nuw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp sge i32 [[I]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp sge i32 [[IPLUS1]], [[LENGTH_I]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nuw i32 %i, 1
+  %var29 = icmp sge i32 %i, %length.i
+  %var30 = icmp sge i32 %iplus1, %length.i
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+;negative case, X + 1 <(u) Y !==> X <(u) Y (X = Y = 0xffffffff)
+define i1 @test_ugt_icmp_no_nuw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_ugt_icmp_no_nuw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp ugt i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp ugt i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add i32 %i, 1
+  %var29 = icmp ugt i32 %length.i, %i
+  %var30 = icmp ugt i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; negative case, X +_{nsw} 1 <(u) Y !==> X <(u) Y (X = 0xffffffff, Y = 0xfffffffe)
+define i1 @test_ugt_icmp_nsw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_ugt_icmp_nsw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nsw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp ugt i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp ugt i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nsw i32 %i, 1
+  %var29 = icmp ugt i32 %length.i, %i
+  %var30 = icmp ugt i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; negative case, X + 1 <=(u) Y !==> X <=(u) Y (X = 0xffffffff, Y = 0x0)
+define i1 @test_uge_icmp_no_nuw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_uge_icmp_no_nuw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp uge i32 [[LENGTH_I:%.*]], [[I]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp uge i32 [[LENGTH_I]], [[IPLUS1]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add i32 %i, 1
+  %var29 = icmp uge i32 %length.i, %i
+  %var30 = icmp uge i32 %length.i, %iplus1
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; negative case, X +_{nsw} 1 <=(u) Y !==> X <=(u) Y
+define i1 @test_uge_icmp_nsw(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_uge_icmp_nsw(
+; CHECK-NEXT:    [[IPLUS1:%.*]] = add nsw i32 [[I:%.*]], 1
+; CHECK-NEXT:    [[VAR29:%.*]] = icmp uge i32 [[I]], [[LENGTH_I:%.*]]
+; CHECK-NEXT:    [[VAR30:%.*]] = icmp uge i32 [[IPLUS1]], [[LENGTH_I]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp ule i1 [[VAR30]], [[VAR29]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %iplus1 = add nsw i32 %i, 1
+  %var29 = icmp uge i32 %i, %length.i
+  %var30 = icmp uge i32 %iplus1, %length.i
+  %res = icmp ule i1 %var30, %var29
+  ret i1 %res
+}
+
+; (X >> Z) <=(u) Y ==> X <=(u) Y
+define i1 @test_shift(i64 %x, i64 %y, i64 %shift) {
+; 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]]
+;
+  %lshr = lshr i64 %x, %shift
+  %icmp1 = icmp ugt i64 %lshr, %y
+  %icmp2 = icmp ugt i64 %x, %y
+  call void @llvm.assume(i1 %icmp1)
+  ret i1 %icmp2
+}
+
+; (X > Y +_{nuw} 1) ==> X != Y
+define i1 @assume_x_ugt_y_plus_1(i64  %x, i64  %y)  {
+; CHECK-LABEL: @assume_x_ugt_y_plus_1(
+; CHECK-NEXT:    [[TMP1:%.*]] = add nuw i64 [[Y:%.*]], 1
+; CHECK-NEXT:    [[TMP2:%.*]] = icmp ugt i64 [[X:%.*]], [[TMP1]]
+; CHECK-NEXT:    tail call void @llvm.assume(i1 [[TMP2]])
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp eq i64 [[X]], [[Y]]
+; CHECK-NEXT:    ret i1 [[TMP3]]
+;
+  %1 = add nuw i64 %y, 1
+  %2 = icmp ugt i64 %x, %1
+  tail call void @llvm.assume(i1 %2)
+  %3 = icmp eq i64 %x, %y
+  ret i1 %3
+}
+
+declare void @llvm.assume(i1)