1. That the bishop of Rome held a unique Petrine office in addition to being a bishop;
2. That this office was instituted by our Lord Himself and given to Peter alone among the Apostles;
3. That the bishops of Rome were the successors to this office;
4. That this office pertained to the universal Church and not just to the church of Rome.
Again, for the moment I do not want to address whether this opinion was valid, nor what the further attributes of this office are, only that this was the belief of the Western church.
Based on the Councils, there was no mention of any of that. Whether the Church in the West believed all that is unknown to me. But I am pretty sure the rest of the Church did not, individual Fathers notwithstanding.