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I have twice successfully claimed for items that I did not have any proof of purchase at all, so you should be ok with any sort of evidence that you purchased the item. Once was for an MP3 player ($200). The other time was for a phone ($400), but I had a letter from the service provider saying that I had reported it stolen and that it was blocked.
I think it really just depends on a case by case basis. Obviously, the more expensive the item, or the less believable that you would be travelling with it, the more evidence they may look for.
Ever since I had something stolen abroad I now just lay out my travel belongings before I pack them and take a picture of the whole lot. For electronics I take note of serial numbers as well. At least this way I'll always have at least some record that I owned and was travelling with the item.