References
- [1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.10.1007/s10817-017-9440-6
- [2] Garrett Birkhoff. Lattice Theory. Providence, Rhode Island, New York, 1967.
- [3] B. I. Dahn. Robbins algebras are Boolean: A revision of McCune’s computer-generated solution of Robbins problem. Journal of Algebra, 208:526–532, 1998.
- [4] B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.
- [5] Adam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211–221, 2015. doi:10.1007/s10817-015-9333-5.10.1007/s10817-015-9333-5
- [6] Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.10.3233/FI-2016-1406
- [7] Adam Grabowski. Robbins algebras vs. Boolean algebras. Formalized Mathematics,9(4): 681–690, 2001.
- [8] Adam Grabowski and Markus Moschner. Managing heterogeneous theories within a mathematical knowledge repository. In Andrea Asperti, Grzegorz Bancerek, and Andrzej Trybulec, editors, Mathematical Knowledge Management Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 116–129. Springer, 2004. doi:10.1007/978-3-540-27818-4_9. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19–21, 2004.10.1007/978-3-540-27818-4_9.3rdSep.19212004
- [9] Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.10.1007/s10817-015-9345-1
- [10] Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. Equality in computer proof-assistants. In Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin, editor, Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, volume 5 of ACSIS-Annals of Computer Science and Information Systems, pages 45–54. IEEE, 2015. doi:10.15439/2015F229.
- [11] George Grätzer. General Lattice Theory. Academic Press, New York, 1978.
- [12] George Grätzer. Lattice Theory: Foundation. Birkhäuser, 2011.
- [13] Violetta Kozarkiewicz and Adam Grabowski. Axiomatization of Boolean algebras based on Sheffer stroke. Formalized Mathematics, 12(3):355–361, 2004.
- [14] W. McCune, R. Padmanabhan, M. A. Rose, and R. Veroff. Automated discovery of single axioms for ortholattices. Algebra Universalis, 52(4):541–549, 2005.
- [15] William McCune. Prover9 and Mace4. 2005–2010.
- [16] William McCune and Ranganathan Padmanabhan. Automated Deduction in Equational Logic and Cubic Curves. Springer-Verlag, Berlin, 1996.
- [17] Ralph McKenzie. Equational bases for lattice theories. Mathematica Scandinavica, 27: 24–38, 1970. doi:10.7146/math.scand.a-10984.10.7146/math.scand.a-10984
- [18] Ranganathan Padmanabhan and Sergiu Rudeanu. Axioms for Lattices and Boolean Algebras. World Scientific Publishers, 2008.
- [19] Piotr Rudnicki and Josef Urban. Escape to ATP for Mizar. In First International Workshop on Proof eXchange for Theorem Proving-PxTP 2011, 2011.
- [20] Marlow Sholander. Postulates for distributive lattices. Canadian Journal of Mathematics, 3:28–30, 1951. doi:10.4153/CJM-1951-003-5.10.4153/CJM-1951-003-5
- [21] Wioletta Truszkowska and Adam Grabowski. On the two short axiomatizations of ortho-lattices. Formalized Mathematics, 11(3):335–340, 2003.
- [22] Stanisław Żukowski. Introduction to lattice theory. Formalized Mathematics,1(1):215–222, 1990.