Why would higher expected inflation increase corporate earnings and dividends' rate of increase? A Random Walk Down Wall Street (2015 11 ed). p. 125.

Determinant 4: The level of market interest rates. The stock market does not exist as a world unto itself. Investors should consider how much profit they can obtain elsewhere. Interest rates, if they are high enough, can offer a stable, profitable alternative to the stock market. Consider periods such as the early 1980s when yields on prime-quality corporate bonds soared to close to 15 percent. The expected returns from stock prices had trouble matching these bond rates; money flowed into bonds while stock prices fell sharply. Finally, stock prices reached such a low level that a sufficient number of investors were attracted to stem the decline. Again in 1987, interest rates rose substantially, preceding the great stock-market crash of October 19. To put it another way, to attract investors from high-yielding bonds, stock must offer bargain-basement prices.*
  *The point can be made another way by noting that because higher interest rates enable us to earn more now, any deferred income should be “discounted” more heavily. Thus, the present value of any flow of future dividend returns will be lower when current interest rates are relatively high. The relationship between interest rates and stock prices is somewhat more complicated, however, than this discussion may suggest. Suppose investors expect that the rate of inflation will increase from 5 percent to 10 percent. Such an expectation is likely to drive interest rates up by about 5 percentage points to compensate investors for holding fixed-dollar-obligation bonds whose purchasing power will be adversely affected by greater inflation. Other things being the same, this should make stock prices fall. $\color{red}{\text{But with higher expected inflation, investors may reasonably project that corporate earnings and dividends will also increase at a faster rate}}$, causing stock prices to rise. A fuller discussion of inflation, interest rates, and stock prices is contained in Chapter 13.

Please expound the sentence that I reddened overhead?
I don’t have the book, but the passage hints that it will be covered in Chapter 13.

The passage has “reasonably project” as a disclaimer, which does imply that it would not hold in all cases. It is not that hard to find counter-examples. If we define inflation as a change in the CPI, oil price spike will normally raise CPI. The higher energy costs are bad for firms with energy input costs, while the oil producers that benefit may be foreigners.

However, if we stick to an idealised scenario, where all prices are rising at roughly the same rate, we can get the result that profits rise in line with inflation. If we make two assumptions:


real activity is not affected by the change in inflation rates;
profit margins are stable.


We then are in a situation where we are just projecting current variables forward with the same real growth rate, while nominal variables are growing by the sum of real growth and inflation. 

If profit margins are stable, then that implies that nominal profits are proportional to nominal revenues, and so would scale with inflation.

The passage implies that the author thinks those two assumptions are reasonable, and presumably detailed in Chapter 13. (I don’t have any references handy, but I’ve certainly seen similar arguments many times. The main difficulty is whether higher inflation is associated with higher or lower profit margin.)