How do CPI linked bonds react (price and yield) to increases in expected inflation in both the short term and long term?

I'm going to attempt to answer my own question- will someone please tell me if my reasoning is correct!

In the short term, increases in anticipated inflation will raise the price of short term inflation linked bonds, as they protect you against the increased inflation, so yield goes down. Long term, the increased inflation in the short term has basically no effect, e.g. an extra 1% inflation in one month time will not make a lot of difference in 20 years. So it behaves like a normal bond, a reduction in price due to the increased nominal interest rate and hence an increased yield.

AM I CORRECT?!

Wow, economics!
Suppose there are two bonds; Bond A that gives you a 10% annual yield and Bond B that offers a CPI+5% yield. As long as your inflation anticipation is 5%, you should be indifferent between these two bonds. Now let's suppose the expected inflation in the market went up to 12%. In this case Bond A isn't a profitable investment tool, consequently all investors will sell their A-Bonds until the yield rises (price falls) to a satisfactory level. In B-bonds there won't be an immediate selling pressure since the yield is automatically adjusted by the CPI indexed return. However, in the long term investors who see more uncertainty (and risk) due to higher inflation may ask for higher spreads and this +5% may not be sufficient for them. Therefore, some sales may be seen.

Makes sense?
Have a great day