Why? I think this would only be true if negative inflation is the goal. Since the inflation rate is computed relative to last year and as long as salaries do not increase, after a year or two of inflation the average employee has less and less disposable income left, so they can spend less unnecessarily and accordingly the inflation could go down to zero despite full employment.

As an example, if I can buy 2 units of a good this year (so demand is high) and then high inflation persists for two years and now I can only afford one unit (so demand is low) - my salary being the same, then an inflation rate of 0 in year 3 would mean everything stays the same. I can still only afford one unit and that should push prices down or at least keep them steady which is what zero inflation would mean.

Maybe the assumption is that decreased demand will necessarily cause unemployment, but this seems to be true only for domestic demand (questionable for the software industry) and in any case following this line of thought would mean the more employment the more inflation which seems absurd.