REM sleep takes place much sooner than 4 hours. It takes place at about 90 minutes of sleep. And, hopefully, the sleeper goes through several cycles throughout the night. I would be screwed if it took that long to get to REM as I wake up 4-5 times a night.
Sorry, you are correct. However when it first takes place, when there is more “deep sleep” work to be done, it is very brief, and becomes the more dominant aspect of sleep after that work has been done:
