A simple "proof" using logic is finding someone who worked really hard and failed (called a proof by contradiction): this is not hard, many have worked really hard and don't have much to show for it. Thus, hard work does not lead to success. But it does enable it.
Similarly, there are plenty of cases where someone was lucky but still blew it up (FTX anyone?). So just like with hard work, luck does not mean guaranteed success. It does, however, enable it.