Proof of what you already own
This article is a travel topic
Although this discussion gives examples for on U.S. customs processes, the basic precepts apply widely.
If you plan to travel to other countries, you don't want pay duty on what you already own and take on your trip, especially valuables. As you return from any international trip, you can be charged duty on all valuables you have with you that exceed your duty exemption.
For fine jewelry, new model cameras, electronics, computers, etc., your government's customs bureau likely offers a means to avoid the problem. As an example for U.S. citizens, you can go to the customs web-site  to get essential information (e.g., "Know Before You Go), and start paperwork that can identify valuables you want to take. For them, the latter steps are essentially...
Original (in the U.S.) store receipts can be a fair substitute for proof of prior ownership if you lack time or access to a customs office before your trip. Even if dated well-before your trip, receipts from overseas sellers often have little standing. Don't count on getting customs forms certified as you depart your country; it takes time and customs officers may be busy.