Upgrading to SRAM Rival from Tiagra 9 Speed
 

All that's needed is:

• Rival right brifter
• Rival RD
• Any Shimano/SRAM 10 speed cassette
• 10 speed chain

Correct?

that would be the bare min but I would get a shifter set personally

Will the RD not work on 10 speed? It is the shifter that determines the RD movement correct? The distance traveled from small ring to big ring is the same isn't it? Just more stops closer together?
These are questions, not statements as I continue my education on bike mechanisims.

Incorrect, you also need to consider the cable pull ratio. With Shimano, they have kept this constant throughout almost all their indexed rear derailleurs (early Dura-Ace is an exception) so any rear derailleur will work with any shifter. SRAM uses a different cable pull ratio, so you must match a SRAM shifter with a SRAM derailleur.

Thanks

Correct. You'll probably need a new cable and possibly housing.

A member of my club is selling only the right because he upgraded to Red and left the left the same; since it's such a good price I'm jumping on it now and will probably wait until I have the cash for a left brifter to actually make the swap. Just wanted to confirm that it would in fact work.