Hilbert Problem 15 and Nonstandard Analysis (I)

Hilbert problem 15 required understanding Schubert's book. In this book, reducing to degenerate cases was one of the main methods for enumeration. We found that nonstandard analysis is a suitable tool for making rigorous of Schubert's proofs of some results, which used degeneration method, but are obviously not rigorous. In this paper, we give a rigorous proof for Example 4 in Schubert's book, Chapter 1. 4 according to his idea. This shows that Schubert's intuitive idea is correct, but to make it rigorous a lot of work should be done.