And the burden of proof is on you, and others who support your position, to prove how a heretic can be the Pope.
No burden at all. The whole world knows that a pope was elected and accepted his election according to the law of the Church. That *is* the proof, just not to sedes.
Me: Catholic dogma and papal teaching states manifest heretics cannot hold office, including the papacy. Therefore, Bergoglio couldn't possibly be the Pope.
You: Heretics can be Pope, and also, heretics are still inside the Church, but we can act like he isn't the Pope as long as we don't say he isn't the Pope.
Well, there is no dogma that states such a thing, but even if there were, there isn't, but if there were, we do not have the authority to expel popes from the Church, nor does his status affect our hope of salvation. Catholics have to obey him as the pope in all those religious matters which fall within the ambit of his authority, unless he should command something which is sinful. Only this way can one never go wrong.
Given that you've already proven that you have a heretical belief that heretics are inside the Church, I don't see you actually proving how a heretic can be the Pope.
No, you are not quoting me properly. From now on, please quote me as saying this: "The simple truth is that Catholics who have fallen into the mortal sin of heresy remain members." It is as Trent's catechism teaches -
"Heretics and schismatics are excluded from the Church, because they have separated from her and belong to her only as deserters belong to the army from which they have deserted." Although they belong to her only as deserters, the catechism says they still belong to her - in spite of their trying to get out of it.
If they want to be absolved of those sins while they're still living, all they need to do is the same thing every other penitent member of the Church does, which is go to confession, a privilege enjoyed only by members of the Church.