1) It is the teaching of the Church through her Universal and Ordinary Magisterium, the unanimous teaching of the Fathers, and the unanimous teaching of the theologians that the public sin of manifest formal heresy by its very nature separates the heretic from the Church. 

COMMENT: That is an easy statement to make, but an impossible statement to prove.  But I will accept quotes from only 2 popes and 5 theologians who taugh that "the public sin of manifest formal heresy by its very nature separates the heretic from the Church."  I bet you can even quote one who uses the phrase "public sin of manifest formal heresy."  That phrase in itself is a post Vatican II novelty that was invented by Fr. Paul Kramer in the last decade.

2) The public sin of manifest formal heresy occurs when one advertently and willingly denies or doubts a teaching of the Church that must be believed with Divine and Catholic Faith.

Comment: I didn't ask for your definition of the novel phrase that Fr. Kramer invented.  I asked for an authoritative definition.  Still waiting. 

3) It should be obvious that Jorge Bergoglio doesn't have a Catholic bone in his body.  Even semi-trads and those of the Novus Ordo acknowledge such. 

Comment: He wakes up in 4:30am and does a holy hour for 2 hours.  He says Mass every day, AND HE DEFENDS CATHOLIC DOCTRINE CONSTANTLY.  If you deny that bolded part, it only proves that you are basing your judgment on him based on what other people are saying or short excepts you are reading, and not by reading what he writes and says on a weekly basis.  The reality is that Bergoglio is no worse than any of the other post-Vatican II popes.
 

4) Garrigou-Lagrange was speaking about occult heresy.  Yes.  He did admit that occult heresy causes one to separate from the Church, but the more common opinion is that occult heresy does not cause one to separate from the Church.  Even so, we do not know his view of public heresy.  It could be that in regards to public heresy, because the separation would be visible, then the putative pope would fall from office. Think about it this way:  since no one (or a few) would know that a occult heretic pope ceased to be a member, Our Lord would retain him as pope until his heresy became public.  I am not saying that this is true.  I am just giving a potential explanation assuming that Garrigou-Lagrange was correct.  Nevertheless, the matter at hand is about public heresy and not occult heresy.

Comment: To be precise, the distinction is not between occult heresy and public heresy; it is between occult heresy and notorious heresy.  Perhaps Francis is in occult herey, but he does not come close to be a notorious heretic; and no one who has taken the time to study the meaning of notorious heresy would deny it.  BTW, how much time have you spent studying the meaning of notorious heresy?

How does the same code of canon law describe "public defection from the faith"?

In fact, the "new" form used in the New Rite of Paul VI, is not only what Pope Clement (either the second or third Pope) said Christ himself gave as the form of episcopal consecration

And if you ever take the time to apply the conditions for a valid form (given by Fr. Cekada)

since the form found in the Traditional Rite does not even come close to meeting them.  For example, if the phrase "dew of heavenly anointing" does not clearly refer to the Holy Ghost, and in fact cannot have any other possible meaning than "the Holy Ghost," then the Traditional Rite of episcopal consecration is absolutely null and utterly void, according to Fr. Cekada.

https://www.mosteirodasantacruz.org/post/dom-vigan%C3%B2-dom-lefebvre-e-o-sedevacantismo

Archbishop Vigano, Archbishop Lefebvre and Sedevacantism

Archbishop Vigano behaved like a real hero from the moment he understood or began to understand the moral and doctrinal decomposition of the Conciliar Church. Unfortunately, he seems to be leaning towards the sedevacantist position. Time will better tell what is his true position.

As for Archbishop Lefebvre, he initiated this fight against the Conciliar Church in more decisive circuмstances than the present ones. He won the confidence of the faithful from all over the world, by the solidity of his formation and the superiority of his prudence. His prudence made him avoid both the ralliement of the Ecclesia Dei communities and the error of Sedevacantism. With precision, he showed how Dom Gérard and others committed ѕυιcιdє by placing themselves under the authority of the Modernists, and how the Sedevacantists, in turn, placed themselves in a position as uncertain as it was dangerous, affirming more than the teachings of the Church allow us to affirm.

Some think that Archbishop Lefebvre would be a Sedevacantist today. I do not think that this is the case. In fact, I believe the opposite. I believe that the arguments he made during his lifetime retain their force and relevance today. His arguments are simple. How would the Church be left if the Popes, from John XXIII to Francis, are not Popes? If the Cardinals they nominated are not Cardinals? Who will then elect the Pope? How can we have a Pope again? This seems to endanger the very existence of the Church. The best thing to do is to wait for the sentence that the Church will one day give, defining and resolving this question.

Faced with the divergence of ideas and practical attitudes within Tradition, I see only one sensible line of conduct to follow: to preserve and transmit what we have received from Archbishop Lefebvre, both from the doctrinal and prudential point of view. But many will say: prudence takes into account the change in the situation between the state of the crisis in the time of Archbishop Lefebvre and the present time. Yes, there are some changes, but they are not essential. The essence of the crisis remains the same.

Like in the Arian crisis, which lasted about 60 years, this crisis continues without changing in essential points. That is why the example of Archbishop Lefebvre is still valid.

May Our Lady, who has overcome all heresies, obtain for us the grace to overcome the attacks of the Devil and the Modernists.

Tomas Aquinas, OSB

https://www.lifesitenews.com/opinion/is-francis-the-pope-the-argument-from-public-heresy-suggests-not/

Actually, I don't agree with the Cassiciacuм Thesis, but anyone who can say this about Bergoglio:

He wakes up in 4:30am and does a holy hour for 2 hours.  He says Mass every day, AND HE DEFENDS CATHOLIC DOCTRINE CONSTANTLY. 

is not a Traditional Catholic.  And I'm judging things as they actually are. 

I would have agreed with you three years ago, since, at the time, like you, I had never bothered to read his sermons and writings. They aren't nearly as bad