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References

  1. [1] Susanne Apel. The geometry of brackets and the area principle. Phd thesis, Technische Universität München, Fakultät für Mathematik, 2014.
  2. [2] Susanne Apel and Jürgen Richter-Gebert. Cancellation patterns in automatic geometric theorem proving. In Automated Deduction in Geometry, pages 1–33. Springer, 2010.10.1007/978-3-642-25070-5_1
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.
  4. [4] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17
  5. [5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990.
  6. [6] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599–603, 1991.
  7. [7] Laurent Fuchs and Laurent Thery. A formalization of Grassmann-Cayley algebra in Coq and its application to theorem proving in projective geometry. In Automated Deduction in Geometry, pages 51–67. Springer, 2010.10.1007/978-3-642-25070-5_3
  8. [8] Kanchun, Hiroshi Yamazaki, and Yatsuka Nakamura. Cross products and tripple vector products in 3-dimensional Euclidean space. Formalized Mathematics, 11(4):381–383, 2003.
  9. [9] Wojciech Leończuk and Krzysztof Prażmowski. A construction of analytical projective space. Formalized Mathematics, 1(4):761–766, 1990.
  10. [10] Wojciech Leończuk and Krzysztof Prażmowski. Projective spaces – part I. Formalized Mathematics, 1(4):767–776, 1990.
  11. [11] Xiquan Liang, Piqing Zhao, and Ou Bai. Vector functions and their differentiation formulas in 3-dimensional Euclidean spaces. Formalized Mathematics, 18(1):1–10, 2010. doi:10.2478/v10037-010-0001-2.10.2478/v10037-010-0001-2
  12. [12] Nicolas Magaud, Julien Narboux, and Pascal Schreck. Formalizing projective plane geometry in Coq. In Automated Deduction in Geometry, pages 141–162. Springer, 2008.10.1007/978-3-642-21046-4_7
  13. [13] Timothy James McKenzie Makarios. A mechanical verification of the independence of Tarski’s Euclidean Axiom. Victoria University of Wellington, New Zealand, 2012. Master’s thesis.
  14. [14] Karol Pąk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199–211, 2007. doi:10.2478/v10037-007-0024-5.10.2478/v10037-007-0024-5
  15. [15] Karol Pąk. Linear transformations of Euclidean topological spaces. Formalized Mathematics, 19(2):103–108, 2011. doi:10.2478/v10037-011-0016-3.10.2478/v10037-011-0016-3
  16. [16] Jürgen Richter-Gebert. Mechanical theorem proving in projective geometry. Annals of Mathematics and Artificial Intelligence, 13(1-2):139–172, 1995.10.1007/BF01531327
  17. [17] Jürgen Richter-Gebert. Perspectives on projective geometry: a guided tour through real and complex geometry. Springer Science & Business Media, 2011.10.1007/978-3-642-17286-1
  18. [18] Wojciech Skaba. The collinearity structure. Formalized Mathematics, 1(4):657–659, 1990.
  19. [19] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990.
DOI: https://doi.org/10.1515/forma-2016-0020 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 239 - 251
Submitted on: Oct 18, 2016
Published on: Feb 23, 2017
Published by: University of Białystok, Department of Pedagogy and Psychology
In partnership with: Paradigm Publishing Services
Publication frequency: 1 times per year

© 2017 Roland Coghetto, published by University of Białystok, Department of Pedagogy and Psychology
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