If you’ve been following my line of reasoning, Paul VI did not say that “infallibility was not used in a solemn manner at the Council”, but that infallibility was not engaged. That’s what his words say. Now, Vatican II had two Dogmatic Constitutions. Vatican I used Dogmatic Constitutions, as Councils do. In order to safeguard previous Councils, we would have to argue that Vatican II offered not a single teaching that was not already infallible in the two Dogmatic Constitutions. This is imperative. Now, the Church as far as I know has only taught with fallible authority that the Pope can bind to fallible teachings, therefore when Vatican II says “In matters of faith and morals, the bishops speak in the name of Christ and the faithful are to accept their teaching and adhere to it with a religious assent. This religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. His mind and will in the matter may be known either from the character of the documents, from his frequent repetition of the same doctrine, or from his manner of speaking”, I’ve interpreted “authentic magisterium” to be infallible but not solemn teachings, and therefore “ex cathedra” merely for solemn teachings. Now, religious submission to a Pope is language now used for fallible teachings, but again there is no common usage of many of these terms among Catholics.