John of St. Thomas:

Objection: We cannot know with certainty of faith that the particular electors have a valid intention of election, nor that they are true and legitimate Cardinals, nor that they observed the form of election required by law, such as the requirement that the Pope be elected by two-thirds majority of the cardinals, as well as the other conditions without which the election is null.

Answer: The acceptance and definition of the Church, inasmuch as it gives the certitude of faith [concerning the legitimacy of the Pope], does not touch upon the conditions of the election, or the intention and genuine identity of the electors, without intermediary, but rather mediately, and as a logical consequence of what it immediately touches upon: namely, that whoever is elected by the persons that the Church designates to choose a Pope in her name, by the very fact that he is accepted by the Church as legitimately elected, is in fact Pope. This latter is what the definition of Martin V, related above, as well as the acceptance of the Church, is really about. Now, from the de fide truth that this man is Pope, it follows as a consequence that all the requisite conditions must have been observed.  For, faith does not concern itself primarily with the conditions that must be realized in the electors, but only afterwards with the person elected [i.e., the object of faith is the legitimacy of the one elected, not whether the conditions required for a valid election were met].  It is the same with the definitions of Councils. Faith is not concerned with the prerequisites of the definition—for instance, that the definition was preceded by diligent investigation, or a disputation about the propositions to be defined—for this is not the subject-matter of faith. Nevertheless, once the definition has been given [which is the object of faith], one rightly infers as a theological conclusion that all the things necessary for the definition were in place, and consequently that there was a discussion preceding it.  (…)

"Likewise, because it is de fide that this man in particular, accepted by the Church as canonically elected, is the Pope, the theological conclusion is drawn that there were genuine electors, and a real intention of electing, as well as the other requisites, without which the de fide truth could not stand.

"Therefore, we have the certainty of faith, by a revelation implicitly contained in the Creed and in the promise made to Peter, and made more explicit in the definition of Martin V, and applied and declared in act (in exercitio) by the acceptance of the Church, that this man in particular, canonically elected according to the acceptance of the Church, is Pope. The certainty of faith touches this alone [i.e., his legitimacy]; and whatever is prerequisite to it [i.e., the conditions], or else follows upon the fact of the election, is inferred as a theological conclusion drawn from the proposition that is de fide, and is believed mediately.

Syllogism:

Major:  Francis' acceptance as pope by the entire Church following his election, provides infallible certitude that he became the legitimate Pope.

Minor:  One of the conditions required for Francis to have become Pope is that the Chair of Peter was vacant at the time, and hence that Benedict’s abdication was valid.

Conclusion: Since Francis was accepted as Pope by the entire Church, this proves infallibly that the Chair of Peter was vacant and hence that Benedict’s abdication was valid.


http://www.trueorfalsepope.com/p/peaceful-and-universal-acceptance-of.html

John of St. Thomas:

"Whoever would deny that a particular man is Pope after he has been peacefully and canonically accepted, would not only be a schismatic, but also a heretic; for, not only would he rend the unity of the Church… but he would also add to this a perverse doctrine, by denying that the man accepted by the Church is to be regarded as the Pope and the rule of faith. Pertinent here is the teaching of St. Jerome (Commentary on Titus, chapter 3) and of St. Thomas (IIa IIae Q. 39 A. 1 ad 3), that every schism concocts some heresy for itself, in order to justify its withdrawal from the Church.  Thus, although schism is distinct from heresy, in most cases it is accompanied by the latter, and prepares the way for it. In the case at hand, whoever would deny the proposition just stated would not be a pure schismatic, but also a heretic, as Suarez also reckons (above, in the solution to the fourth objection)."[10]

• according to religious usage, with due observances, with proper ceremonies, ceremonially, solemnly, duly

Sean, as I have said in that other thread. John of St. Thomas is dealing with how the infallible teaching authority of the Church (through a Pope or a valid Ecuмenical Council) can quiet all concerns regarding unknowns in a previous papal election. Any such controversy can be settled by an infallible authority of the Church declaring a "dogmatic fact." The Church did that at the Council of Constance, which is what John of St. Thomas references.

However, there has been no infallible declaration of a Pope or an Ecuмenical Council that Jorge Mario Bergolio is the legitimate Pope. This has not happened. And it would never happen because his 2013 "election" was null and void. There is no question. It is obvious.

The particular "dogmatic fact" in the above examples is that Pius X, the specific man, was the true Pope. In his case, there was no controversy. But with Gregory XII there was controversy. The Council of Constance settled the controversy and declared/defined a "dogmatic fact" that Gregory XII was the Pope prior to Martin V. The Council of Constance was the example that John of St. Thomas used.