The Mizar system is one of the pioneering systems aimed at supporting mathematical proof development on a computer that have laid the groundwork for and eventually have evolved into modern interactive proof assistants. We claim that an important milestone in the development of these systems was the creation of organized libraries accumulating all previously available formalized knowledge in such a way that new works could effectively re-use all previously collected notions. In the case of Mizar, the turning point of its development was the decision to start building the Mizar Mathematical Library as a centrally-managed knowledge base maintained together with the formalization language and the verification system. In this paper we show the process of forming this library, the evolution of its design principles, and also present some data showing its current use with the modern version of the Mizar proof checker, but also as a rich corpus of semantically linked mathematical data in various areas including web-based and natural language proof presentation, maths education, and machine learning based automated theorem proving.
This special issue is dedicated to works related to Mizar, the theorem proving project started by Andrzej Trybulec in the 1970s, and other automated proof checking systems used for formalizing mathematics.
In this paper we prove that every collineation of the Segre product of strongly connected partial line spaces is (up to permutation of indices) the product of collineations of its components (Thm. 1.10). Spaces of pencils are strongly connected, so the claim holds for Segre products of them (Thm. 1.14). In the second part we study the extendability of collineations of Segre products of spaces of pencils under some natural embeddings. (2000): 51A45, 51M35.
Mathematics Subject Classification
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