That is what happened to me.
The graphic on the right was my “friend” for nearly 2.5 hours Tuesday afternoon [from about 2:10 – 4:20 pm EDT].
Thanks to Terri Clevenger, AppleCare iOS & Mac Senior Advisor, and some luck, I recovered and went on to complete the installation.
I learned that others had this problem as well. Apple said:
The issue has been “quickly resolved” and impacted a small number of users during the first hour of availability. In the meantime, if you haven’t done so already, you should back up your iPhone before downloading iOS 10.