It's a copy with your memories, not you. Is one of them still you, if we make three copies?

they're also just you, but with a different derivative.

This is roughly inline with a many-worlds theorem where tiny variations can create many versions of you, this would be that but within the same universe.

Well, proving it would require you to end your life because the basis for the theorem is that there will always be a version of you that will not die.