Understanding Schubert's book (I)

Hilbert Problem 15 required an understanding of Schubert's book [1], both its methods and its results. In this paper, following his idea, we prove that the formulas in 6, 7, 10, about the incidence of points, lines and planes, are all correct. As an application, we prove formulas 8 and 9 in 12, which are frequently used in his book.

Automated summary

This paper proves the correctness of formulas regarding the incidence of points, lines, and planes in sections 6, 7, and 10, following the ideas presented in Schubert's book. Additionally, formulas 8 and 9 in section 12, which are frequently used in the book, are also proven as an application.