The Chinese Remainder Theorem, its Proofs and its Generalizations in Mathematical Repositories

In the spirit of mathematical knowledge management theorems are proven with computer assistance to be included into mathematical repositories. In the mathematical literature one often finds not only different proofs for theorems, but also different versions or generalizations with a different background. In mathematical repositories, for obvious reasons, there is usually one version of a theorem with one proof only — the authors choose a version and a proof which can be formalized most easily. In this paper we argue that there are other issues to decide which proof of a theorem or which version of a theorem should be included in a repository. These basically depend on the intended further use of the theorem and the proof. We illustrate these issues in detail with the Chinese Remainder Theorem as an example.