Improving Mizar Texts with Properties and Requirements

  • Adam Naumowicz
  • Czesław Byliński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3119)

Abstract

In this paper we report on the current state of implementation of two features of the Mizar system – properties and requirements. These two mechanisms provide elements of basic computer algebra to strengthen the capabilities of the Mizar checker by automation of some frequently used reasoning steps. This, in turn, allows for a notable reduction of the size of users’ input in some reasonings. As a result, the size of the Mizar library can be reduced, and, at the same time, Mizar articles can become more like informal mathematical papers.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bancerek, G.: The Fundamental Properties of Natural Numbers. Journal of Formalized Mathematics 1 (1989), http://mizar.org/JFM/Vol1/nat_1.html
  2. 2.
    Bancerek, G.: Sequences of Ordinal Numbers. Journal of Formalized Mathematics, http://mizar.org/JFM/Vol1/ordinal2.html
  3. 3.
    Bancerek, G.: The Ordinal Numbers. Journal of Formalized Mathematics, http://mizar.org/JFM/Vol1/ordinal1.html
  4. 4.
    Byliński, C.: Some Basic Properties of Sets. Journal of Formalized Mathematics, http://mizar.org/JFM/Vol1/zfmisc_1.html
  5. 5.
    Library Committee. Basic Properties of Real Numbers - Requirements. Journal of Formalized Mathematics, Requirements (2003), http://mizar.org/JFM/Reqmnts/real.html
  6. 6.
    Library Committee. Basic Properties of Subsets - Requirements. Journal of Formalized Mathematics, Requirements (2003), http://mizar.org/JFM/Reqmnts/subset.html
  7. 7.
    Library Committee. Boolean Properties of Sets – Definitions. Journal of Formalized Mathematics, Encyclopedia of Mathematics in Mizar (2002), http://mizar.org/JFM/EMM/xboole_0.html
  8. 8.
    Library Committee. Boolean Properties of Sets - Requirements. Journal of Formalized Mathematics, Requirements (2002), http://mizar.org/JFM/Reqmnts/boole.html
  9. 9.
    Library Committee. Complex Numbers – Basic Definitions. Journal of Formalized Mathematics, Encyclopedia of Mathematics in Mizar (2003), http://mizar.org/JFM/EMM/xcmplx_0.html
  10. 10.
    Library Committee. Field Properties of Complex Numbers - Requirements. Journal of Formalized Mathematics, Requirements (2003), http://mizar.org/JFM/Reqmnts/arithm.html
  11. 11.
    Library Committee. Introduction to Arithmetic of Real Numbers. Journal of Formalized Mathematics, Encyclopedia of Mathematics in Mizar (2003), http://mizar.org/JFM/EMM/xreal_0.html
  12. 12.
    Library Committee. Mizar Built-in Notions. Journal of Formalized Mathematics, Axiomatics (1989), http://mizar.org/JFM/Axiomatics/hidden.html
  13. 13.
    Library Committee. Numerals – Requirements. Journal of Formalized Mathematics, Requirements (2003), http://mizar.org/JFM/Reqmnts/numerals.html
  14. 14.
    Hryniewiecki, K.: Basic Properties of Real Numbers. Journal of Formalized Mathematics, http://mizar.org/JFM/Vol1/real_1.html
  15. 15.
    Naumowicz, A., Byliński, C.: Basic Elements of Computer Algebra in MIZAR. Mechanized Mathematics and Its Applications 2, 9–16 (2002), http://markun.cs.shinshu-u.ac.jp/mizar/mma.dir/2002/MMA_2002_paper_2_for_web.html Google Scholar
  16. 16.
    Popiołek, J.: Some Properties of Functions Modul and Signum. Journal of Formalized Mathematics, http://mizar.org/JFM/Vol1/absvalue.html
  17. 17.
    Rudnicki, P., Trybulec, A.: On Equivalents of Well-Foundedness. An Experiment in MIZAR. Journal of Automated Reasoning 23, 197–234 (1999)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Trybulec, A.: Tarski Grothendieck Set Theory. Journal of Formalized Mathematics, http://mizar.org/JFM/Axiomatics/tarski.html
  19. 19.
    Trybulec, Z.: Properties of Subsets. Journal of Formalized Mathematics, http://mizar.org/JFM/Vol1/subset_1.html
  20. 20.
    Wiedijk, F.: Checker. Available on: http://www.cs.kun.nl/~freek/notes/by.ps.gz
  21. 21.
    Woronowicz, E.: Relations and Their Basic Properties. Journal of Formalized Mathematics, http://mizar.org/JFM/Vol1/relat_1.html

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Adam Naumowicz
    • 1
  • Czesław Byliński
    • 2
  1. 1.Institute of Computer ScienceUniversity of BiałystokPoland
  2. 2.Section of Computer Systems and Teleinformatic NetworksUniversity of BiałystokPoland

Personalised recommendations