This, May 10th, being the Feast of Saint Antoninus I thought I would include his declaration of Church teaching if a pope were ever to become a heretic AFTER a valid election.
St Antoninus (1459)
"In the case in which the pope would become a heretic, he would find himself, by that fact alone and without any other sentence, separated from the Church. A head separated from a body cannot, as long as it remains separated, be head of the same body from which it was cut off. A pope who would be separated from the Church by heresy, therefore, would by that very fact cease to be head of the Church. He could not be a heretic and remain pope, because since he is outside of the Church, he cannot possess the keys of the Church."
Summa Theologica, cited in Actes de Vatican I. V. Frond, publisher.
To the contrary---while the five key teachings of Jansenism were ultimately defined as heresy by the church, it did in fact originate as a theological movement within the Catholic Church, associated with Cornelius Jansen, the bishop of Ypres. It gained significant popularity with the French Cistercian sisters as well as Catholic philosophers such as Pascal who criticized what they regarded as growing Pelagianism in the Church due to the influence of the Jesuits. They were gravely in error, but in practice they were every bit as Catholic as the Sedevacantists. Their error was in fact the same---they believed that they had the right to cast private but binding judgement regarding who in the Church was a heretic and who was not.
St Antoninus (1459) "In the case in which the pope would become a heretic, he would find himself, by that fact alone and without any other sentence, separated from the Church. A head separated from a body cannot, as long as it remains separated, be head of the same body from which it was cut off. A pope who would be separated from the Church by heresy, therefore, would by that very fact cease to be head of the Church. He could not be a heretic and remain pope, because since he is outside of the Church, he cannot possess the keys of the Church."
That's all true enough; but there's a bit of an asterisk there. Namely, that it is not for private individuals to determine whether or not the Pope is a material heretic, nor is it for them to decide to reject his office or declare his Papacy invalid. To quote John of Saint Thomas' summary of Saint Jerome's comments on this topic:
" St. Jerome---in saying that a heretic departs on his own from the Body of Christ---does not preclude the Church's judgment, especially in so grave a matter as is the deposition of a pope. He refers instead to the nature of that crime, which is such as to cut someone off from the Church on its own and without other censure in addition to it---yet only so long as it should be declared by the Church...So long as he has not become declared to us juridically as an infidel or heretic, be he ever so manifestly heretical according to private judgment, he remains as far as we are concerned a member of the Church and consequently its head. Judgment is required by the Church. It is only then that he ceases to be pope as far as we are concerned".
Again, you cannot unilaterally decide that the Pontiff is invalid based upon your own private judgement that he is heretic. That was the error of Bishop Jansen and the many Catholics he led into schism, and that is also manifestly the error of the Sedevacantists.