I don't need to prove what is self-evident and accepted by all. If the Catholic Church is not the original Church Christ founded, then from what did it spring, and where did the Church Christ found go? We don't need such childish nonesense. The Reformers openly admitted that their revolt was not over a disbelief in the lineage of the Church of Rome, but over doctrinal disputes where they felt Rome had strayed from the Apostles. You are more than free to believe as they do, but please don't try to push the cockamamie line that the Catholic Church is not the direct descendant of the Apostolic and Patristic Church.
(As opposed to, say, the Orthodox Church.)
The Roman Catholic Church believes the Eastern Orthodox are dissident Catholics who are still essentially part of the same Church. This is why we recognize the validity of their jurisdictional rulings, and do not dispute their characterization of themselves as Catholics in their confessions and creeds. Our dispute is best characterized as a family squabble.