I think you need to find a better way to say what you realy mean, bro. Because it sounds like you refuse to listen to reason & that you are trying to minimize & marginalize the Two Swords doctrine in that Bull.
It does not explicitly limit Papal temporal authority to Christendom:
" Therefore, if the Greeks or others should say that they are not confided to Peter and to his successors, they must confess not being the sheep of Christ, since Our Lord says in John 'there is one sheepfold and one shepherd.' We are informed by the texts of the gospels that in this Church and in its power are two swords; namely, the spiritual and the temporal. For when the Apostles say: 'Behold, here are two swords' [Lk 22:38] that is to say, in the Church, since the Apostles were speaking, the Lord did not reply that there were too many, but sufficient. Certainly the one who denies that the temporal sword is in the power of Peter has not listened well to the word of the Lord commanding: 'Put up thy sword into thy scabbard' [Mt 26:52]. Both, therefore, are in the power of the Church, that is to say, the spiritual and the material sword, but the former is to be administered _for_ the Church but the latter by the Church; the former in the hands of the priest; the latter by the hands of kings and soldiers, but at the will and sufferance of the priest. "
So don't ever believe it when you hear the Inquisition executions weren't RCC because they were performed by secular authorities.
The Two Swords Doctrine is about as full as a faith could get, but not a faith in God, in my humble opinion.