St. Robert Bellarmine really takes pains in this passage to assert and prove more than once that a pope who falls into heresy is no longer the pope, even without a declaration.
Yeti, what about this teaching of St Robert in his work On Councils? The first few paragraphs provide some context. Does it not add anything to the debate? Don't you think there is a role for the Church to play before we can make this definitive judgement?:
1... the particular reasons , on account of which Councils are celebrated, are usually numbered as six... d) the fourth reason is suspicion of heresy in the Roman Pontiff, if perhaps it might happen, or if he were an incorrigible tyrant; for then a general Council ought to be gathered either to depose the Pope if he should be found to be a heretic, or certainly to admonish him, if he seemed incorrigible in morals... general Councils ought to impose judgment on controversies arising in regard to the Roman Pontiff - albeit not rashly... e) the fifth reason is doubt about the election of a Roman Pontiff... (from Ch IX On the utility or even the necessity of celebrating Councils)
2. It is certain that hitherto a Council has never been called for this purpose. The same can be said about the fourth reason. For on account of suspicions on the doctrine and life of Popes, no Council has been convened apart from provincial or national Councils. Nor does it seem necessary for a greater Council; for while the Pope is truly a pope, he cannot be judged by any Council, unless he himself were to grant the power... and it could impose a judgement of the Council, but not a coercive judgement... (from Ch X General Councils are useful and in a certain measure necessary, but not absolutely and simply)
3. Catholics customarily propose certain doubts... The second, whether or not it is lawful for a Council to be summoned by anyone other than the Pope when the Pope cannot summon it, for the reason that he is a heretic or schismatic... I respond that in no case can a true and perfect Council (such as we make our disputation on here) be convoked without the authority of the Pope, because he has the authority to define questions of faith. For the particular authority is in the head, in Peter... for whom the Lord prayed lest his faith would fail (Luke 22). Still, in those two cases an imperfect Council could be gathered which would suffice to provide for the Church from the head. For the Church, without a doubt, has the authority to provide for itself from the head... Hence, that imperfect Council can happen, if either it is summoned by the college of Cardinals, or the Bishops themselves come together in a place of themselves. (from Ch XIV Certain doubts are answered)
4. The Lutherans... propose eight conditions for celebrating a Council... Firstly,... the Council of Trent be invalidated. Secondly, that the Council be in Germany... Thirdly, that the Roman Pontiff should not summon the Council, nor preside in it, but that it should be on the other side of those litigating, just as when someone is accused and no man is at the same time the judge and the accusing party... The third condition is unjust, because the Roman Pontiff cannot be deprived of his right to summon Councils and preside over them...
unless he were first convicted by the legitimate judgement of a Council and is not the Supreme Pontiff. Moreover, what they say, that the same man ought not be a judge and a party, I say has place in private men, but not in a supreme prince.
For the supreme prince, as long as he is not declared or judged to have legitimately been deprived of his rule, is always the supreme judge, even if he litigates with himself as a party. (from Ch XXI The conditions which the Lutherans require to celebrate a Council are refuted)