diff --git a/src/cmd/compile/internal/ssa/prove.go b/src/cmd/compile/internal/ssa/prove.go
index 172d210216e..10a16917b67 100644
--- a/src/cmd/compile/internal/ssa/prove.go
+++ b/src/cmd/compile/internal/ssa/prove.go
@@ -248,6 +248,16 @@ func (ft *factsTable) update(parent *Block, v, w *Value, d domain, r relation) {
 				lim.min = c
 				lim.max = c
 			}
+			if lim.min >= 0 {
+				// int(x) >= 0 && int(x) >= N  ⇒  uint(x) >= N
+				lim.umin = uint64(lim.min)
+			}
+			if lim.max != noLimit.max && old.min >= 0 && lim.max >= 0 {
+				// 0 <= int(x) <= N  ⇒  0 <= uint(x) <= N
+				// This is for a max update, so the lower bound
+				// comes from what we already know (old).
+				lim.umax = uint64(lim.max)
+			}
 		case unsigned:
 			var uc uint64
 			switch w.Op {
@@ -281,6 +291,9 @@ func (ft *factsTable) update(parent *Block, v, w *Value, d domain, r relation) {
 				lim.umin = uc
 				lim.umax = uc
 			}
+			// We could use the contrapositives of the
+			// signed implications to derive signed facts,
+			// but it turns out not to matter.
 		}
 		ft.limitStack = append(ft.limitStack, limitFact{v.ID, old})
 		lim = old.intersect(lim)
diff --git a/test/prove.go b/test/prove.go
index 2f4fa5d308c..13e18cd7280 100644
--- a/test/prove.go
+++ b/test/prove.go
@@ -479,12 +479,33 @@ func sm1(b []int, x int) {
 	// Test constant argument to slicemask.
 	useSlice(b[2:8]) // ERROR "Proved slicemask not needed$"
 	// Test non-constant argument with known limits.
-	// Right now prove only uses the unsigned limit.
-	if uint(cap(b)) > 10 {
+	if cap(b) > 10 {
 		useSlice(b[2:]) // ERROR "Proved slicemask not needed$"
 	}
 }
 
+func lim1(x, y, z int) {
+	// Test relations between signed and unsigned limits.
+	if x > 5 {
+		if uint(x) > 5 { // ERROR "Proved Greater64U$"
+			return
+		}
+	}
+	if y >= 0 && y < 4 {
+		if uint(y) > 4 { // ERROR "Disproved Greater64U$"
+			return
+		}
+		if uint(y) < 5 { // ERROR "Proved Less64U$"
+			return
+		}
+	}
+	if z < 4 {
+		if uint(z) > 4 { // Not provable without disjunctions.
+			return
+		}
+	}
+}
+
 //go:noinline
 func useInt(a int) {
 }