I'm looking to upgrade our TV Set from a 1080p screen to a 4K set-up. Not sure if this a home theater question or Mini.. Currently we have a Mac mini 2012 2.5Ghz 16GB RAM and AppleTV 3 hooked up to our set. If I introduce a 4K screen and connect it via HDMI to either the TV3 or Mac mini will it even show anything? will it downscale to the most appropriate resolution for each device?