Something like, “for all branches, [...]”? That might be not that easy to prove or even to formulate. In any case, the linked proof has not even started to deal with this.
Something like, “there exist a branch such that [...]”? That might be quite tractable, but probably not enough for practical purposes.
“The probability that one ends up in a branch with such and such properties is no less than/no more than” [...]? Probably something like that, realistically speaking, but this still needs a lot of work, conceptual and mathematical...
yes one can—all of them!
Yes, but then what do you want to prove?
Something like, “for all branches, [...]”? That might be not that easy to prove or even to formulate. In any case, the linked proof has not even started to deal with this.
Something like, “there exist a branch such that [...]”? That might be quite tractable, but probably not enough for practical purposes.
“The probability that one ends up in a branch with such and such properties is no less than/no more than” [...]? Probably something like that, realistically speaking, but this still needs a lot of work, conceptual and mathematical...