Read the relevant parts of the ADA here in the U.S. and you'll see that he has no need to *prove* his cat is a service animal. All business owners have the right to do is to ask, "are you disabled?" and, "is this a service animal?" If you answer yes to either point, they are obliged to let the animal in. There are service cats/dogs/birds/snakes/etc. out there and they all do good. It's a damn shame when non-disabled people are so judgmental.

I spent some time in Cappadocia a few years back and it's an amazing place!