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.