Well, my rephrasing was meant to be more than just s/validity/liveness/: I find that removing quantifiers (like for-all) often improves my understanding, as it

Well, my rephrasing was meant to be more than just s/validity/liveness/: I find that removing quantifiers (like for-all) often improves my understanding, as it usually gives more obvious context/motivation for what the goal is. It is then easier to understand the more formal version once I know approximately what it is trying to do.