Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

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

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

- Preliminaries
- More on Ordering Relations
- Foundedness Properties

- [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.

[ Download a postscript version, MML identifier index, Mizar home page]