Hornby library seems now to be on Smarts Road near the corner with Waterloo Road, here:
https://www.openstreetmap.org/?mlat=-43.5390&mlon=172.5249#map=16/-43.5390/172.5249&layers=N

Source:
https://my.christchurchcitylibraries.com/locations/HORNBY/

I have visited it, and either the source is correct or I was very confused.