John of St. Thomas wrote (here he describes the issue of occult heresy regarding a Pope as well as the two conditions that are needed in order to depose a Pope for heresy):

Two Conditions

"But we need to know if the Pope can be deposed in any case of heresy and in whatever form of being a heretic.; or if some additional conditions are needed without which heresy alone is not sufficient to depose the Pontiff.

I answer that the Pontiff cannot be deposed and lose his pontificate except if two conditions are fulfilled together:

1) That the heresy is not hidden, but publicly and legally notorious;

2) then that he must be incorrigible and pertinacious in his heresy.

If both conditions are fulfilled the Pontiff may be deposed, but not without them; and even if he is not unfaithful interiorly, however if he behaves externally as a heretic, he can be deposed and the sentence of deposition will be valid.

Concerning the first requirement, among some Catholics are of a different opinion, saying that even for occult heresy [Editor: occult = "hidden," "not visible"], the Pontiff loses his Papal jurisdiction, which is based on the true Faith and right confession of Faith; supporting this opinion we have Torquemada (1,2p. from v. 18 and 1. 2, c. 102) Paludanus, Castro, Simancus, Driedo […]

Others think that it is necessary that the heresy must be external and proved in the external forum in order that the Pontiff can be deposed of the pontificate; thus Soto (4 sent. D. 22 q.2.2); Cano (from Locis 1.4), who believes that the contrary opinion is not even probable; Catejan (On the pope's power, De Comparatione auctoritatis papae and concilii cuм apologia eiusdem tractatus, Rome, Angelicuм, 1936; c.18 and 19), Suarez, Azorius, Bellarmine (On the Roman Pontiff, c.30).

The principle is that occult heretics, as long as they are not condemned by the Church and being separated [by her] belong to the Church and are in communion with her, as like being moved from the exterior, even if they do not receive any more interiorly the vital movement; therefore, the Pontiff, if he is an occult heretic, is not separated from the Church; therefore, he can still be the head, since he is still a part and a member, even if he is not a living one.

A confirmation of it is that priests of a lower order can exercise the power of order and jurisdiction without Faith because a heretical priest can confer the sacraments in cases of extreme need […]

The second condition, in order to be able to depose the Pope, namely that he is guilty of incorrigible and pertinacious heresy, is evident, because if someone is ready to be corrected and is not pertinacious in heresy, is not considered to be heretical (Decree of Gratian, No. 24. 3. 29 "Dixit Apostolus"); therefore, if the Pope is ready to be corrected, he should not be deposed as a heretic.

The Apostle [Paul] prescribes to avoid heretics only after a first and second correction: if he comes to repentance after the correction, he should not be avoided; therefore, as the Pope must be deposed for heresy under this apostolic precept, it follows that if he can be corrected, he should not be deposed."

http://www.dominicansavrille.us/on-the-deposition-of-the-pope-part-1-of-2/

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Fr. Kramer's name is on the diploma issued by Holy Apostles College and Seminary on 1 August 1988; signed by Fr. Francis Lescoe (President and Rector, Fr. Bradley Pierce (Secretary, Board of Directors), Sr. Mary Reagan (Academic Dean), and Bro. Daniel Karempelis (Registrar). A photo of the diploma will appear presently on my facebook page.

Salza and Sicoe's entire mis-interpretation of Bellarmine rests on arbitrarily restricting Bellarmine's reference to defecting from the Church on his own to someone who formally apostasizes.

This is rejected by the Canon Lawyers who have commented on the related canons.

https://stevensperay.wordpress.com/2016/03/17/canon-188-4-and-defection-of-faith-why-john-salza-and-robert-siscoe-get-it-wrong-part-iii/

All the Canonists agree that both apostasy AND heresy constitute a defection from faith (in the context of the canon under discussion) ... whether there being some dispute among the canonists whether schism that does not involve heresy counts as defection from the faith.

And the Canonists also agree that the resignation from office is not "in the nature of a penalty".

I think that the confusion is this ...

MAJOR:  Legitimate Pope cannot become a heretic.
MINOR:  Bergoglio is a heretic.
CONCLUSION:  Therefore, Bergoglio was never a legitimate pope.

I would add:
MAJOR: A heretic (non Catholic) cannot validly be elected pope
MINOR:  Bergoglio was a heretic before his “election”.
CONCLUSION:  Therefore, Bergoglio was never a legitimate pope.

On the Deposition of the Pope

Please stop spamming that article into this thread piece by piece.  It's obnoxious forum behavior.  Anyone could find an article representing their point of view and spam it in.  I could easily take the contents of that link I posted just above and spam the entire thing in here also.

All the Canonists agree that both apostasy AND heresy constitute a defection from faith (in the context of the canon under discussion) 

Of course, Ladislaus.  But what's under dispute is WHEN is one guilty of heresy?  PaxChristi2's research argues that this does not apply until the Church rules on the matter.  I agree.  Once the Church discerns heresy, THEN that person has defected from the faith (or, it can be said that it is established as fact that they defected).
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The way you explained it above is too general.  It glosses over a few steps which must take place first.  It's a summary with no detailed process.  

So....it's getting to you that your beloved opinions are being refuted here. Well, that's how forums work, Ladislaus.

No, that is not how forums work.  They are intended for discussion and argument, not spamming in entire articles, piece by piece, peppering them in without any regard for whether or not they are pertinent to the current state of the thread.