You'd need to prove that a DBMS executes a query always correctly to begin with. That in itself would be quite the task. Additionally SQL as supported by some

You'd need to prove that a DBMS executes a query always correctly to begin with. That in itself would be quite the task. Additionally SQL as supported by some DBMSes (e.g. Postgres due to recursive CTE and window functions) is turing complete. That makes proving equivalency in general a bit challenging.