Can you use Apple Care+ without any checks (bringing just MacBook)?
Solution 1:
Yes, they confirm AppleCare status in their system, and you don’t need to provide anything else.
At least, that has been my experience.
Solution 2:
You can simply go the Apple Store and ask them to repair. You can say that it has Apple Care and they will verify it with your serial number.
No need to show any kind of paper. I have done 2 times already.