Yes, like I said before, one would have to refer to the theological sources that Father includes in his bibliography for a more lengthy description; however, I have read other things Father has written that explains and applies those differences.  They can also be found on the internet. 

It seems to me that you never read the whole article he wrote when you linked it in the OP.  Otherwise, you wouldn't have asked me to explain his position and post what you had already posted.

Regardless, I'm not arguing with you about this.  

I read the article and read "that divine law prevents a heretic from becoming a true pope (or remaining one, if a pope embraces heresy during the course of his pontificate.)"

Which divine law? Divine law is a law or revelation given to us directly from God, such as the 10 commandments for example.

So which divine law prevents a heretic from becoming pope?

Divine law is either ius divinum positivum or ius divinum naturale, depending on whether it is revealed or known by reason itself based on the nature of things.

it is absurd to imagine that he who is outside can command in the Church.

Calling the proposition absurd, Leo XIII implies that it is known by reason itself that he who isn't even a member, cannot be head; hence this is ius divinum naturale.

For not every offense, although it may be a grave evil, is such as by its very own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy.

Pius XII says that schism, heresy, and apostasy are offenses which by their very own nature sever a man from the body of the Church. We don't need a revelation to recognize that schism, heresy, and apostasy on the one hand, and Church membership on the other hand, are incompatible. A Church member confesses the faith; a schismatic, heretic, or apostate confesses ideas contrary to the faith.

it is proven with arguments from authority and from reason that the manifest heretic is "ipso facto" deposed.
[...]
This principle is most certain. The non-Christian cannot in any way be Pope, as Cajetan himself admits (ib. c. 26). The reason for this is that he cannot be head of what he is not a member; now he who is not a Christian is not a member of the Church, and a manifest heretic is not a Christian, as is clearly taught by St. Cyprian (lib. 4, epist. 2), St. Athanasius (Scr. 2 cont. Arian.), St. Augustine (lib. de great. Christ. cap. 20), St. Jerome (contra Lucifer.) and others; therefore the manifest heretic cannot be Pope.

The reason, St. Robert gives, is: "he cannot be head of what he is not a member". Thus, we know by reason itself, that a heretic cannot in any way be Pope: ius divinum naturale.

Oversimplification.  There are various types of heresy, and there are 2 types of Church membership.

I was answering the question "So which divine law prevents a heretic from becoming pope?", and not writing a dissertation about possible classifications of heretics.

+Bellarmine even says that an occult heretic is still a member of the church externally, so he can still hold office, externally.  Lots of distinctions to be made, and you are ignoring them.

St. Robert says: "he cannot be head of what he is not a member".

Divine law is either ius divinum positivum or ius divinum naturale, depending on whether it is revealed or known by reason itself based on the nature of things.

I mean *which* divine law? What is needed is, say for example, against the 1st or 2nd or ? commandment, or reference the pertinent divine revelation from Scripture, this is what is necessary.  To say anything is against Divine Law necessarily must at least be able to reference the specific Divine Law itself.

Quote from: Leo XIII, Satis cognitum

Quote

it is absurd to imagine that he who is outside can command in the Church.

Calling the proposition absurd, Leo XIII implies that it is known by reason itself that he who isn't even a member, cannot be head; hence this is ius divinum naturale.

The problem is the pope, albeit arguably, is not outside.

Quote from: Pius XII, Mystici corporis

Quote

For not every offense, although it may be a grave evil, is such as by its very own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy.

Pius XII says that schism, heresy, and apostasy are offenses which by their very own nature sever a man from the body of the Church. We don't need a revelation to recognize that schism, heresy, and apostasy on the one hand, and Church membership on the other hand, are incompatible. A Church member confesses the faith; a schismatic, heretic, or apostate confesses ideas contrary to the faith.

"Nor must one imagine that the Body of the Church, just because it bears the name of Christ, is made up during the days of its earthly pilgrimage only of members conspicuous for their holiness, or that it consists only of those whom God has predestined to eternal happiness. It is owing to the Savior's infinite mercy that place is allowed in His Mystical Body here below for those whom, of old, He did not exclude from the banquet.

He *then* goes on to say:

For not every sin, however grave it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy."

You did not post the immediately preceding (bolded) parts to put the final sentence in context, where Pope Pius XII said that place is allowed in the Body of the Church for those whom Christ Himself did not exclude from the banquet (Mat. 9:11/footnote) and basically, that the Body of the Church includes sinners. Heresy is a sin, a heretic is a sinner. 

He then reminds us that, to some degree at least, *all* sin severs man from the Body of the Church - which is true, no? But the sin of schism or heresy or apostasy severs a man from the Body of the Church worse than other sins because of the nature of those particular sins.

Quote from: St. Robert Bellarmine, De Romano Pontifice

Quote

it is proven with arguments from authority and from reason that the manifest heretic is "ipso facto" deposed.
[...]
This principle is most certain. The non-Christian cannot in any way be Pope, as Cajetan himself admits (ib. c. 26). The reason for this is that he cannot be head of what he is not a member; now he who is not a Christian is not a member of the Church, and a manifest heretic is not a Christian, as is clearly taught by St. Cyprian (lib. 4, epist. 2), St. Athanasius (Scr. 2 cont. Arian.), St. Augustine (lib. de great. Christ. cap. 20), St. Jerome (contra Lucifer.) and others; therefore the manifest heretic cannot be Pope.

The reason, St. Robert gives, is: "he cannot be head of what he is not a member". Thus, we know by reason itself, that a heretic cannot in any way be Pope: ius divinum naturale.

The problem here is, he *is* pope. Our knowledge of his sins of heresy in no way give us the authority to declare otherwise. Thankfully, God did not grant us either supreme nor various degrees of authority based on what we know. Can you imagine it otherwise?  

And he also qualified this statement many different ways, which you apparently are unaware of or ignore.
.
Bellarmine: “Occult heretics are still of the Church, they are parts and members… therefore the Pope who is an occult heretic is still Pope. This is also the opinion of the other authors whom we cite in book De Ecclesia. …the occult heretics are united and are members although only by external union; on the contrary, the good catechumens belong to the Church only by an internal union, not by the external”.

No, I'm not unaware. I just don't clutter up my post about divine law with distinctions, which are irrelevant in the given situation.

Thankfully, God did not grant us either supreme nor various degrees of authority based on what we know. Can you imagine it otherwise?  

Yes, I can imagine it otherwise, because that's the situation that we are in with so many sedevacantists who rely on their own judgment in believing that they do have the authority to depose a pope. And now the sedes may say that heresy is not actually a sin. Or it's not the same thing as other sins.

Another interesting consideration is this.

Take the case of a heretic priest, say, in the 1950s.  He's running around obstinately preaching heresy.  There were many of these already in the 1950s.  Does that priest still have jurisdiction to hear Confession?  Or has he been so thoroughly severed from the Church that he can no longer do so, since he's no member of the Church?

I would say that this priest still has jurisdiction because he's a conduit for the bishop's jurisdiction ... until the bishop were to relieve him of duty.

Now take the case of a heretic bishop, like, say, Cardinal Cushing.  Did he have jurisdiction or did he lose it?  Were all the priests in the Diocese of Boston then lacking in jurisdiction since Cushing was radically outside the Church?  I would again hold that Cushing retained jurisdiction because he was a conduit for papal jurisdiction, since all jurisdiction flows from the pope.

But would Cushing then have any real authority?  Or is he just a passive/material conduit for jurisdiction?

Now take it up to the Pope.  So, some theologians hold that even an Antipope could continue to serve as a conduit for jurisdiction (which comes from Christ) ... probably based on similar reasoning.  This actually addresses the "ecclesiavacantist" argument against sedevacantism.  In the case of an Antipope, bishops could still have ordinary jurisdiction flowing from Christ through the passive/material conduit of the Antipope, and then any bishops who were not themselves severed from the Church could actually exercise ordinary jurisdiction.

So that's my view of things, that Bergoglio is a material pope and that he serves as a material conduit for jurisdiction, even though he has no jurisdiction himself ... and he certainly lacks any teaching authority due to his heresy.