Well, if you look around on wnyrails.org, it appears as if the TV&C and its successor the BA&A was bought by the B&S to run from Wellsville to Buffalo. So, you have TV&C building in 1880, 1881 from Attica to Currier to Arcade, Sandusky, Freedom, Rushford, Hardy Corners, Rawson, and Cuba (and perhaps south to Hinsdale). They went bankrupt in 1894 and immediately became the BA&A standard-gauged from Attica to Arcade then west to Yorkshire and south to Sandusky. Then in 1904 they were sold to the B&S for their Wellsville to Buffalo line. In 1916 all was torn up and sold for scrap. Not clear what happened to the Attica to Arcade line while the B&S owned it. Clearly, though, the B&S sold it to the Arcade and Attica intact, along with the branch line to the PRR in Yorkshire.
To add to the fun, the TV&C predecessor, the Attica and Allegheny Valley Railroad, graded most of the route between Attica and Arcade, although they ran out of money before they could lay rail. How much do you want to bet that the TV&C built on the A&AV grade? Now THAT would be difficult to prove. Might be do-able with lots and lots of research in the county clerk's office. Let's say that you found a bit of railbed between Arcade and Attica which wasn't A&A. How could you tell if it was relocated from TV&C, or TV&C relocated from A&AV.
Quite a puzzle!