There is a question of system - in some countries, "professor" is a separate title convened by national body, and is separate from whatever status you have at y

There is a question of system - in some countries, "professor" is a separate title convened by national body, and is separate from whatever status you have at your individual teaching organization - for example, in Poland, we have "professor extraordinary", which is lower rank and convened by specific university and not valid outside, and "professor ordinary", which is presented to you by president after recommendation from scientific body - and is valid everywhere. Both of those titles require having a second-level doctorate (meaning you also did a "habilitation"), but are separate titles and when writing it down formally you're supposed to write them separately