Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Dickson's Lemma


Gilbert Lee
University of Alberta, Edmonton
Piotr Rudnicki
University of Alberta, Edmonton

Summary.

We present a Mizar formalization of the proof of Dickson's lemma following [7], chapters 4.2 and 4.3.

MML Identifier: DICKSON

The terminology and notation used in this paper have been introduced in the following articles [29] [11] [35] [22] [36] [38] [28] [37] [15] [30] [3] [33] [34] [8] [26] [27] [5] [32] [2] [1] [24] [16] [17] [10] [9] [20] [25] [19] [14] [31] [23] [4] [18] [12] [6] [13] [21]

Contents (PDF format)

  1. Preliminaries
  2. More on Ordering Relations
  3. Foundedness Properties

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. The well ordering relations. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[5] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[6] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[7] Thomas Becker and Volker Weispfenning. \em Gr\"obner Bases: A Computational Approach to Commutative Algebra. Springer-Verlag, New York, Berlin, 1993.
[8] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[12] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[13] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.
[14] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[15] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[16] Agata Darmochwal and Andrzej Trybulec. Similarity of formulae. Journal of Formalized Mathematics, 3, 1991.
[17] Adam Grabowski. Auxiliary and approximating relations. Journal of Formalized Mathematics, 8, 1996.
[18] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[19] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.
[20] Jaroslaw Kotowicz. Monotone real sequences. Subsequences. Journal of Formalized Mathematics, 1, 1989.
[21] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[22] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[23] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[24] Jan Popiolek. Real normed space. Journal of Formalized Mathematics, 2, 1990.
[25] Jan Popiolek. Introduction to Banach and Hilbert spaces --- part III. Journal of Formalized Mathematics, 3, 1991.
[26] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.
[27] Piotr Rudnicki and Andrzej Trybulec. On same equivalents of well-foundedness. Journal of Formalized Mathematics, 9, 1997.
[28] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[29] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[30] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[31] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[32] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[33] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[34] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Journal of Formalized Mathematics, 1, 1989.
[35] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[36] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[37] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[38] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

Received March 12, 2002


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