Ok,
I have attempted to detail this library... 

The building base is https://www.openstreetmap.org/way/1292752686 - this carries the tags for the library. It should have the highest level tagged on it.. I think arr yes .. https://wiki.openstreetmap.org/wiki/Key:building:part

I think I have it right, please check it!
Other than the base library way above the 2 other ways are ;
https://www.openstreetmap.org/way/205303849
https://www.openstreetmap.org/way/159946355
