diff --git a/crates/recursion/core/src/chips/alu_base.rs b/crates/recursion/core/src/chips/alu_base.rs
index 4a1b10abcc..6acb1b73c5 100644
--- a/crates/recursion/core/src/chips/alu_base.rs
+++ b/crates/recursion/core/src/chips/alu_base.rs
@@ -209,6 +209,10 @@ where
         ) in zip(local.values, prep_local.accesses)
         {
             // Check exactly one flag is enabled.
+            builder.assert_bool(is_add.clone());
+            builder.assert_bool(is_sub.clone());
+            builder.assert_bool(is_mul.clone());
+            builder.assert_bool(is_div.clone());
             let is_real = is_add + is_sub + is_mul + is_div;
             builder.assert_bool(is_real.clone());
 
diff --git a/crates/recursion/core/src/chips/alu_ext.rs b/crates/recursion/core/src/chips/alu_ext.rs
index 462cc55d96..860280ac3b 100644
--- a/crates/recursion/core/src/chips/alu_ext.rs
+++ b/crates/recursion/core/src/chips/alu_ext.rs
@@ -214,6 +214,10 @@ where
             let out = vals.out.as_extension::<AB>();
 
             // Check exactly one flag is enabled.
+            builder.assert_bool(is_add.clone());
+            builder.assert_bool(is_sub.clone());
+            builder.assert_bool(is_mul.clone());
+            builder.assert_bool(is_div.clone());
             let is_real = is_add + is_sub + is_mul + is_div;
             builder.assert_bool(is_real.clone());