That’s far from certain. A surprising number of 4K devices will downscale high resolution still images to 1080p, then upscale them again, losing detail in the process. This can be hard to see with regular photos, so here is a 4K test image that makes things completely clear. It consists of four bundles of horizontal lines and four bundles of vertical lines, with twelve in each bundle, and a different colour for each horizontal bundle and each vertical bundle. The whole image is 3,840 pixels wide by 2,160 pixels tall.
Each line is only one pixel thick and the space between the ten inner lines of each bundle is also only one pixel thick. The two outer lines are two pixels away from the inner lines.
There are also some markers near the screen boundaries to show if there is any overscan at all. Here’s a detail of the centre of the image:
If your device is delivering full 4K, you will see it on your TV’s screen precisely defined with those spaces between the lines. But if your device is downscaling to 1080p at some point in the chain, then that definition will disappear and this is what you will see:
To get the full image, right click here and choose the appropriate item to save the image.