diff --git a/crates/proof-of-sql/src/base/database/join_util.rs b/crates/proof-of-sql/src/base/database/join_util.rs
index 363b704b2..d8e274f10 100644
--- a/crates/proof-of-sql/src/base/database/join_util.rs
+++ b/crates/proof-of-sql/src/base/database/join_util.rs
@@ -102,16 +102,17 @@ fn get_sort_merge_join_indexes<'a, S: Scalar>(
                     })
                     .collect();
 
+                // Advance the iterators
+                left_iter.nth(left_group.len() - 1);
+                right_iter.nth(right_group.len() - 1);
+
                 // Generate all pairs (Cartesian product)
                 let pairs: Vec<_> = left_group
                     .iter()
-                    .flat_map(|&l| right_group.iter().map(move |&r| (l, r)))
+                    .cartesian_product(right_group.iter())
+                    .map(|(&lidx, &ridx)| (lidx, ridx))
                     .collect();
 
-                // Advance the iterators
-                left_iter.nth(left_group.len() - 1);
-                right_iter.nth(right_group.len() - 1);
-
                 Some(pairs)
             }
         }