Funnily enough i was thinking about this the other day, The obvious answer would be to show your receipt from the purchase of the bike, but if it was a long while ago and you've lost it, or you don't keep receipts then something else would have to do. Slight marks on the bike known only to you, would be proof i suppose. For example i know where i've touched up the paint chips and on one of my bikes and there's a slight crack on the frame just below the saddle stem. If the plod wanted to really dig deep i'd tell them to get their fingerprint crew down, My old prints must be on every inch of the bike.