So long as he has confidence that the inflation adjustment will reflect his personal rate of inflation in retirement, he can simply subtract the value of the annuity from the amount of annual spending he needs to cover, which will reduce how much investment he needs to cover the rest.
Example: $80,000 household spending would normally require a stash of $2M. If he has a $50,00 inflation indexed annuity/pension, he'd only need $30,000 of other spending and a stash of only $750,000.
Using the normal way we simulate retiree spending in retirement, having an inflation adjusted annuity doesn't mean he can spend a higher percent of his starting retirement savings and have the same confidence about not running out of money.
That said, having a baseline level of money coming in each month gives him greater flexibility to cut or eliminate his withdrawals from his other retirement funds during recessions and stock market crashes. If he's willing and able to do that, it is possible to withdraw more than 4% safely if you only withdraw and spend that money in good years but not in bad years.