No one has proven or shown that the Bishops possessed infallibility. The Bishops either were or were not infallibly correct in their votes. If they were that is one thing. If they weren’t.... that is another.
And please, no circular reasoning in trying to prove that the Bishops possessed infallibility.
But in any case, the idea is not that the infallibility inheres in a person or persons but in certain situations. The Pope or the bishops who are going to or leaving from a council do not have infallibility as a personal possession or quality.
The basis of the IDEA is that God protects the Church from error. So when it exercises its highest teaching (or “Magisterial”) function, it does so reliably. So questions about the infallibility of the bishops involved do not really touch the question except insofar as they help clarify it.