What I Think:
All children of any age will be able to use the library irrespective of whether or not they are accompanied by an adult. Using the library equates to observing the libraries T&Cs. It is assumed that the parent holds responsibility for their child in the library whether or not they are accompanied by an adult. If the parent is not aware their child is using the library, it is assumed the child is safer in a library than not.
What Libraries Say:
Young children are not allowed to use the library without being accompanied by an older child.
What Libraries Should Say:
Children aged X years or younger cannot use the library unless they are accompanied by an adult who is at least Y years old and who will take full responsibility for them. Children aged between X & Y can use the library without an adult provided that they are not using the library with children aged X years or younger. Children aged Y years and over are considered adults.
(With thanks to the EasyJet T&Cs page)