Inflation makes people rich?

Here in Japan there are some people who insist that rise in prices boost up the economy. 
The reasoning is:

Rise in prices of goods and services increases the sales, the sellers' profit and incomes. Higher income increases their spending on goods, and thus the prices. The people will become richer than before.

It sounds reasonable, but it's totally wrong!

Rise in prices of goods and services increases the sales, the sellers'monetary profit and incomes, but the real value of their incomes doesn't change at all: 10% increase in prices leads to 10% increase in monetary income, but the real income, which is evaluated as how much goods and services people can buy, is the same as before the rise in prices. The people won't become richer than before but stay the same.

These people oppose that if monetary policymaker makes the inflation higher, he or she can make lower the real rate of interest, which is the cost of building houses and machines for production, and thus can make people invest more in those durable goods.

However, I can oppose to such an opposition too;

If monetary policymaker makes higher the inflation, the lenders make the rate of interest as high as the announced inflation rate because they must understand the inflation decreases the real value of their lending, and thus monetary policymaker doesn't make lower the real rate of interest and doesn't induce people to spend more.

However, I don't mean that monetary policy doesn't influence the spending at all. It is until they understand that the real income and real interest rate are not changed that monetary policy is effective on the spending.

And so monetary policy does make the people spend more by lowering the real rate of interest, but its effect will soon be weaker as people get to understand that the inflation deteriorate the real value of the money they hold in the pocket.