Types of proof you may have could depend on the nature of the relationship. If you were married its obvious a divorce certificate. If you were living together maybe a copy of the old lease with both of your names and now an updated one without your ex partners name, same with any bills you previously shared and now do not, old car insurance documents if you were on the same policy before as well as the updated one, etc....
If these do not apply, maybe any old emails between you both that indicate you broke up? Phone bills that show previous calls back and forth to each other's cell numbers leading up to the breakup and afterward to reflect when you stopped calling each other?
If you use that facebook status feature perhaps you can screenshot when you changed that to "in a relationship" with them and later to "no longer in a relationship" with that person and when you changed your status to "in a relationship" with your new partner.
Screenshots of old texts that show prove you broke up, emails or texts with you and other significant people in your life discussing your breakup or referring to your "ex" .. App conversations or texts with your new partner where you may have discussed your previous relationship.
If you don't have much tangible proof which can sometimes be difficult if you were not married or living together, you could maybe write a sworn affidavit explaining the circumstances, when you were in a relationship with said person, and when the relationship ended. Get it notarized. Even letters from close family members declaring you are no longer with that ex and since when they knew about it.
Just a few ideas, hope some of that is helpful