Castlegate old tram lines

Riding past road works at West Bar end of Castlegate today, there was what looked like old tram rails being excavated. Did the original tram lines go through there?

1954 large scale map of the area ... www.sheffieldhistory.co.uk/forums

Here is a link to a picturesheffield.com photo showing the tram lines going from West Bar along Bridge Street. The Bridge Street section was not used much during the ordinary working day but there were some early morning trams, intended for shift workers, that ran from the Hillsborough area to the East End, and these turned left at the points visible in the photo.