This is extremely important. The Church's declaratory sentence is not what causes the loss of power. It merely declares the truth that the manifest heretic "pope" lost his power through divine law. It merely recognizes what has already happened.
Exactly. They fall by their own hand. They fall by their own acts. They fall by their own knowingly false words.
St. Robert Bellarmine, Doctor of the Church: "For, in the first place, it is proven with arguments from authority and from reason that the manifest heretic is "ipso facto" deposed."
St Robert Bellarmine, "De Romano Pontifice", ("On the Roman Pontiff"), liber II, caput 30:
"For, in the first place, it is proven with arguments from authority and from reason that the manifest heretic is "ipso facto" deposed. The argument from authority is based on St. Paul (Titus, c. 3), who orders that the heretic be avoided after two warnings, that is, after showing himself to be manifestly obstinate - which means before any excommunication or judicial sentence. And this is what St. Jerome writes, adding that the other sinners are excluded from the Church by sentence of excommunication, but the heretics exile themselves and separate themselves by their own act from the body of Christ. Now, a Pope who remains Pope cannot be avoided, for how could we be required to avoid our own head? How can we separate ourselves from a member united to us?
"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.
Est ergo quinta opinio vera, papam haereticum manifestum per se desinere esse papam et caput, sicut per se desinit esse christianus et membrum corporis Ecclesiae; quare ab, Ecclesia posse eum judicari et puniri. Haec est sententia omnium veterum Patrum, qui docent, haereticos manifestos mox amittere omnem jurisdictionem.
"Therefore, the true opinion is the fifth, according to which the Pope who is manifestly a heretic ceases by himself to be Pope and head, in the same way as he ceases to be a Christian and a member of the body of the Church; and for this reason he can be judged and punished by the Church. This is the opinion of all the ancient Fathers, who teach that manifest heretics immediately lose all jurisdiction,
Fundamentum hujus sententiae est. quoniam haereticus manifestos nullo modo est membrum Ecclesiae, idest, neque animo neque corpore, sive neque unione interna, neque externa.
"The foundation of this argument is that the manifest heretic is not in any way a member of the Church, that is, neither spiritually nor corporally, which signifies that he is not such by internal union nor by external union.
St. Alphonsus de Liguori, Doctor of the Church, on the fate of a heretical pope:
"Del resto, si Dio permettesse che un papa fosse notoriamente eretico e contumace, egli cesserebbe d'essere papa, e vacherebbe il pontificato."
--"Verita della Fede", part 3, ch. 8, no. 10. In: Opere dommatiche di S. Alfonso de Liguori (Torino, G. Marietti, 1848), p. 720. (Opere di S. Alfonso Maria de Liguori, v. 8)
"For the rest, if God should permit that a Pope should become a notorious and contumacious heretic, he would cease to be Pope, and the pontificate would be vacant."
St. Francis de Sales, Doctor of the Church, on papal infallibility and heresy:
"En l'ancienne loy le grand pretre ne portait pas le rational si non quand il estoit revestu des habits pontificaux et qu'il entroit devant le Seigneur. Ainsi ne disons nous pas que le pape en ses opinions particulieres ne puisse errer comme fit Jean XXII, ou etre du tout heretique comme peut etre fut Honorius. Or quand il est heretique expres *ipso facto* il tombe de son grade hors de l'Eglise et l'Eglise le doit ou priver comme disent quelques uns, ou le declarer prive de son siege apostolique et dire comme fit St. Pierre: Episcopatum eius accipiat alter. Quand il erre en sa particuliere opinion il le faut enseigner, adviser, convaincre comme on fit a Jean XXII le quel tant s'en faut qu'il mourut opiniatre ou que pendant sa vie il determina aucune chose touchant son opinion, que pendant qu'il faysoit l'inquisition requise pour determiner en matiere de foy, il mourut, au recit de son successeur en l'Extravagante qui se commence *Benedictus Deus.*"
St. Francis de Sales, The Catholic Controversy (Tan Books), p. 388 (part II, art. VI, ch. 14)
"Under the ancient law the High Priest did not wear the Rational except when he was vested in the pontifical robes and was entering before the Lord. Thus we do not say that the Pope cannot err in his private opinions, as did John XXII; or be altogether a heretic, as perhaps Honorius was. Now when he is explicitly a heretic, he falls ipso facto from his dignity out of the Church, and the Church must either deprive him, as some say, or declare him deprived, of his Apostolic See, and must say as St. Peter did: Let another take his bishopric (Acts I). When he errs in his private opinion he must be instructed, advised, convinced; as happened with John XXII, who was so far from dying obstinate or from determining anything during his life concerning his opinion, that he died whilest he was making the examination which is necessary for determining in a matter of faith, as his successor declared in the *Extravagantes* which begins Benedictus Deus." (Ib. p. 305-306)
St. Thomas Aquinas, Doctor of the Church, on loss of jurisdiction by heretics and schismatics:
Summa, 2a 2ae, q. 39, art. 3. (Utrum schismatici habeant aliquam potestatem)
"...Potestas autem iurisdictionis est quae ex simplici iniunctione hominis confertur; et talis potestas non immobiliter adhaeret; unde in schismaticis et haereticis non manet; unde non possunt nec absolvere, nec excommunicare, nec indulgentias facere, aut aliquid huiusmodi; quod si fecerint, nihil est actum."
(Whether schismatics have any power.)
"...The power of jurisdiction, however [as opposed to the power of Orders, which he has just discussed], is that [power] which is conferred simply by the injunction of man; and this power does not adhere immovably; therefore it does not remain in schismatics and heretics. Hence they can neither absolve, nor excommunicate, nor grant indulgences, or anything of this sort. If they do this, the act is null."