Add the people to a group. Add the group to the Lib, and give RO. (Or use multiple groups or just the All Authenticated Users.)
By default, any object (list) obtains the site permissions by default.(if the site defaults to the parent site rights, then move that statement up one level.) But, it doesn't work the way you've specified.
I think spending a couple hours reading about permissions would be a good thing before moving forward any further.
Steve Clark, MCTS | Twin-Soft.com