If bitcoin is still in circulation, then proving is easy. If it is a relic, and something of interesting collectible nature, then it would be like proving your tablet IOU from the BC times is legit.
But in any case, most users have a hard time understanding cryptocurrency systems. Thus, it would be very easy to provide bogus info which looks convincing to a layperson. And because fakes would be common, it would take extra care to _really_ prove your collection is real.
This statement could not be further from the truth. It's far easier and more reliable to prove that you own an authentic Bitcoin than it is to prove that you own an authentic painting.
In fact, Bitcoin is the most auditable asset in the history of mankind. The audit process can be done in a decentralized way and carries 0 risk and unlike the auditing processes of other valuable assets, it can be carried out quickly, cheaply and at any scale.
All other auditing processes rely on trusting a third party, not Bitcoin. It's the perfect asset.
Sooner or later, the reserve banks of the world are going to be forced onto cryptocurrencies. Bitcoin is better than gold in terms of supply inelasticity and auditability; these are the two most important features from a reserve asset. Bitcoin is also gaining ground in terms of universal recognition which is the third most important feature.