On Equivalents of Well-Foundedness: An Experiment in MIZAR

Journal of Automated Reasoning

Volumn 23, Issue 3, 1999, Pages 197-234

  Rudnicki, Piotr ^a   Trybulec, Andrzej ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF BIALYSTOK   (Poland)

Author keywords

MIZAR; QED project; Regular cardinals; Set theory; Well foundedness

Indexed keywords

COMBINATORIAL MATHEMATICS; DATABASE SYSTEMS; MATHEMATICAL MODELS; RECURSIVE FUNCTIONS; SOFTWARE ENGINEERING; THEOREM PROVING;

MECHANIZED DATA BASE FOR MATHEMATICS; MIZAR; REGULAR CARDINALS; SYSTEMATIC DEVELOPMENT; WELL FOUNDEDNESS;

SET THEORY;

EID: 0033327714     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006218513245     Document Type: Article

References (53)

1. Bancerek, G.: Directed sets, nets, ideals, filters, and maps, Formalized Mathematics, 1997, to appear.
2. Bancerek, G.: Cardinal numbers, Formalized Mathematics 1(2) (1990), 377-382.
3. Bancerek, G.: The ordinal numbers, Formalized Mathematics 1(1) (1990), 91-96.
4. Bancerek, G.: Sequences of ordinal numbers, Formalized Mathematics 1(2) (1990), 281-290.
5. Bancerek, G.: The well ordering relations, Formalized Mathematics 1(1) (1990), 123-129.
6. Bancerek, G.: Zermelo theorem and axiom of choice, Formalized Mathematics 1(2) (1990), 265-267.
7. Bancerek, G.: Countable sets and Hessenberg's theorem, Formalized Mathematics 2(1) (1991), 65-69.
8. Bancerek, G.: König's lemma, Formalized Mathematics 2(3) (1991), 397-402.
9. Bancerek, G.: On powers of cardinals, Formalized Mathematics 3(1) (1992), 89-93.
10. Bancerek, G. and Hryniewiecki, K.: Segments of natural numbers and finite sequences, Formalized Mathematics 1(1) (1990), 107-114.
11. Bancerek, G. and Trybulec, A.: Miscellaneous facts about functions, Formalized Mathematics 5(4) (1996), 485-492.
12. Białas, J.: Group and field definitions, Formalized Mathematics 1(3) (1990), 433-439.
13. Białas, J. and Nakamura, Y.: The theorem of Weierstrass, Formalized Mathematics 5(3) (1996), 353-359.
14. Boyer, R. S.: A mechanically proof-checked Encyclopedia of Mathematics: Should we build one? Can we? in A. Bundy (ed.), 12th International Conference on Automated Deduction LNAI/LNCS 814, Springer-Verlag, 1994, pp. 237-251.
15. Byliński, C.: A classical first order language, Formalized Mathematics 1(4) (1990), 669-676.
16. Byliński, C.: Functions and their basic properties, Formalized Mathematics 1(1) (1990), 55-65.
17. Byliński, C.: Partial functions, Formalized Mathematics 1(2) (1990), 357-367.
18. Byliński, C.: Some basic properties of sets, Formalized Mathematics 1(1) (1990), 47-53.
19. Darmochwał, A.: Finite sets, Formalized Mathematics 1(1) (1990), 165-167.
20. Darmochwał, A.: Calculus of quantifiers: Deduction theorem, Formalized Mathematics 2(2) (1991), 309-312.
21. Darmochwał, A. and Nakamura, Y.: Heine-Borel's covering theorem, Formalized Mathematics 2(4) (1991), 609-610.
22. de la Cruz, A.: Fix point theorem for compact spaces, Formalized Mathematics 2(4) (1991), 505-506.
23. Franzén, T.: Teaching mathematics through formalism: A few caveats, in D. Gries (ed.), Proceedings of the DIMACS Symposium on Teaching Logic, DIMACS, 1996. On WWW: http://dimacs.rutgers.edu/Workshops/Logic/program.html.
24. Gries, D. and Schneider, F. B.: A Logical Approach to Discrete Math., Springer-Verlag, 1994.
25. Harrison, J.: Inductive definitions: Automation and application, in Proceedings of the 1995 International Workshop on Higher Order Logic Theorem Proving and Its Applications, Lecture Notes in Comput. Sci. 971, Springer-Verlag, 1995, pp. 200-213.
26. Harrison, J.: A Mizar mode for HOL, in J. von Wright, J. Grundy, and J. Harrison (eds.), Theorem Proving in Higher Order Logics: 9th International Conference, TPHOLs'96, Turku, Finland, Lecture Notes in Comput. Sci. 1125, Springer-Verlag, 1996, pp. 203-220.
27. Hayden, S. and Kennison, J. F.: Zermelo Fraenkel Set Theory, Charles E. Merrill Publishing Co., Columbus, Ohio, 1968.
28. Hryniewiecki, K.: Basic properties of real numbers, Formalized Mathematics 1(1) (1990), 35-40.
29. Hryniewiecki, K.: Recursive definitions, Formalized Mathematics 1(2) (1990), 321-328.
30. Jaśkowski, S.: On the rules of supposition in formal logic, Studia Logica 1 (1934).
31. Korolkiewicz, M.: The de l'Hospital theorem, Formalized Mathematics 2(5) (1991), 675-678.
32. Kotowicz, J., Raczkowski, K. and Sadowski, P.: Average value theorems for real functions of one variable, Formalized Mathematics 1(4) (1990), 803-805.
33. Kusak, E.: Desargues theorem in projective 3-space, Formalized Mathematics 2(1) (1991), 13-16.
34. Lamport, L.: How to write a proof, Research Report 94, DEC Systems Reserach Center, Palo Alto, CA, 1993.
35. McCall, S. (ed.): Polish Logic in 1920-1939, Clarendon Press, Oxford, 1967.
36. Nowak, B. and Trybulec, A.: Hahn-Banach theorem, Formalized Mathematics 4(1) (1993), 29-34.
37. Ono, K.: On a practical way of describing formal deductions, Nagoya Math. J. 21 (1962).
38. Popiołek, J.: Real normed space, Formalized Mathematics 2(1) (1991), 111-115.
39. Rudnicki, P. and Trybulec, A.: How to write a proof, Technical Report 96-08, University of Alberta, Department of Computing Science, 1996. 19 pages.
40. Rudnicki, P. and Trybulec, A.: Fix-points in complete lattices, Formalized Mathematics (1997), to appear.
41. Tarski, A.: On well-ordered subsets of any set, Fund. Math. 32 (1939), 176-183.
42. Trybulec, A.: Built-in concepts, Formalized Mathematics 1(1) (1990), 13-15.
43. Trybulec, A.: Function domains and Fraenkel operator, Formalized Mathematics 1(3) (1990), 495-500.
44. Trybulec, A.: Tarski Grothendieck set theory, Formalized Mathematics 1(1) (1990), 9-11.
45. Trybulec, W A.: Partially ordered sets, Formalized Mathematics 1(2) (1990), 313-319.
46. Trybulec, W. A.: Subgroup and cosets of subgroups, Formalized Mathematics 1(5) (1990), 855-864.
47. Trybulec, W. A. and Bancerek, G.: Kuratowski-Zorn lemma, Formalized Mathematics 1(2) (1990), 387-393.
48. Trybulec, Z. and Świȩczkowska, H.: Boolean properties of sets, Formalized Mathematics 1(1) (1990), 17-23.
49. Walijewski, J. S.: Representation theorem for Boolean algebras, Formalized Mathematics 4(1) (1993), 45-50.
50. Watanabe, T.: The Brouwer fixed point theorem for intervals, Formalized Mathematics 3(1) (1992), 85-88.
51. Woronowicz, E.: Relations and their basic properties, Formalized Mathematics 1(1) (1990), 73-83.
52. Woronowicz, E.: Relations defined on sets, Formalized Mathematics 1(1) (1990), 181-186.
53. Żynel, M.: The Steinitz theorem and the dimension of a vector space, Formalized Mathematics 5(3) (1996), 423-428.