I'm not sure that is going to be true of the stock market. Many firms now have record cash holdings[0] so by buying stock you are essentially buying a slice of a pile of money. I argue the reason many firms stock price keeps going up hasn't been a rise in demand but instead a limit on supply as stock buybacks are also at record levels[1].
Inflation doesn't cause the real value of investments to increase, because the real value is the nominal value relative to general prices (and inflation is increase in general prices.)
That's true in the general sense, but low interest rates lead to higher inflation AND better stock market performance. So having lower interest rates benefits people with stock market portfolios and hurts people who have mostly cash.
