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Mizar Analysis of Algorithms: Algorithms over Integers Cover

Mizar Analysis of Algorithms: Algorithms over Integers

Open Access
|Mar 2009

References

  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  2. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  3. [3] Grzegorz Bancerek. Countable sets and Hessenberg's theorem. Formalized Mathematics, 2(1):65-69, 1991.
  4. [4] Grzegorz Bancerek. Joining of decorated trees. Formalized Mathematics, 4(1):77-82, 1993.
  5. [5] Grzegorz Bancerek. Mizar analysis of algorithms: Preliminaries. Formalized Mathematics, 15(3):87-110, 2007.
  6. [6] Grzegorz Bancerek and Piotr Rudnicki. On defining functions on trees. Formalized Mathematics, 4(1):91-101, 1993.
  7. [7] Grzegorz Bancerek and Piotr Rudnicki. Two programs for scm. Part I - preliminaries. Formalized Mathematics, 4(1):69-72, 1993.
  8. [8] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.
  9. [9] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.
  10. [10] Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras. Formalized Mathematics, 4(1):23-27, 1993.
  11. [11] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  12. [12] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  13. [13] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  14. [14] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.
  15. [15] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  16. [16] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  17. [17] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  18. [18] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.
  19. [19] Jarosław Kotowicz, Beata Madras, and Małgorzata Korolkiewicz. Basic notation of universal algebra. Formalized Mathematics, 3(2):251-253, 1992.
  20. [20] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  21. [21] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.
  22. [22] Yatsuka Nakamura and Andrzej Trybulec. On a mathematical model of programs. Formalized Mathematics, 3(2):241-250, 1992.
  23. [23] Beata Perkowska. Free universal algebra construction. Formalized Mathematics, 4(1):115-120, 1993.10.1016/0012-365X(93)90569-F
  24. [24] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.
  25. [25] Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
  26. [26] Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.
  27. [27] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  28. [28] Andrzej Trybulec. Function domains and Frænkel operator. Formalized Mathematics, 1(3):495-500, 1990.
  29. [29] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  30. [30] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  31. [31] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  32. [32] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
DOI: https://doi.org/10.2478/v10037-008-0024-0 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 177 - 194
Published on: Mar 20, 2009
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2009 Grzegorz Bancerek, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 16 (2008): Issue 2 (June 2008)