[1/2] If you want to know where all of this comes from, this shows the lineage:
The first place to start would be the Divinely revealed definition of Vatican I concerning Papal infallibility, which states:
"We teach and define as a divinely revealed dogma that when the Roman pontiff speaks ex cathedra, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his church to enjoy in defining doctrine concerning faith or morals. Therefore, such definitions of the Roman pontiff are of themselves, and not by the consent of the church, irreformable.”
Vatican II, in
Lumen Gentium Section 25, interpreting this infallibility, states:
“And this is the infallibility which the Roman Pontiff… enjoys when… by a definitive act he proclaims a doctrine of faith or morals. And therefore his definitions… are justly styled irreformable… therefore they need no approval of others, nor do they allow an appeal to any other judgment.”
Canon Law furthers this interpretation with Can. 749 §1, stating:
“By virtue of his office, the Supreme Pontiff possesses infallibility in teaching when as the supreme pastor and teacher of all the Christian faithful, who strengthens his brothers and sisters in the faith, he proclaims by definitive act that a doctrine of faith or morals is to be held."
Canon 750 §2, describing our obligation in these matters, states:
“Each and every thing which is proposed definitively by the magisterium of the Church concerning the doctrine of faith and morals, that is, each and every thing which is required to safeguard reverently and to expound faithfully the same deposit of faith, is also to be firmly embraced and retained; therefore, one who rejects those propositions which are to be held definitively is opposed to the doctrine of the Catholic Church.
Therefore, everything that is proposed to be held definitively is to be held as an infallible, irreformable truth.
The Pope, in his authority to bind upon the Faithful by a definitive act, is not limited by a number of miracles, nor a “reduced rigor”, as some would argue. Rather, this authority, as Divinely revealed by Vatican I and expounded upon by Vatican II, is exercised in virtue of his supreme apostolic authority when defining a doctrine on Faith and morals, which also includes truths “intimately connected” with the Faith and truths “with which they are connected either for historical reasons or by a logical relationship” to Faith and morals. Indeed, the “communion of Saints” is so fundamental to Faith that we must profess it, with Divine Faith under penalty of heresy, in the Apostles’ Creed.