Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
K\"onig's Lemma

Grzegorz Bancerek

Warsaw University, Bialystok

Partially supported by RPBP.III24.C1.
Summary.

A continuation of [3].
The notion of finiteorder trees, succesors of an element of a tree,
and chains, levels and branches of a tree are introduced.
That notion has been used to formalize K\"onig's Lemma which claims that
there is a infinite branch of a finiteorder tree if the tree has arbitrary
long finite chains.
Besides, the concept of decorated trees is introduced and
some concepts dealing with trees are applied to decorated trees.
MML Identifier:
TREES_2
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[8]
[13]
[4]
[14]
[6]
[2]
[12]
[5]
[9]
[1]
[7]
[10]
[3]
Contents (PDF format)
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.
Introduction to trees.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [13]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received January 10, 1991
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