Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
The Contraction Lemma
-
Grzegorz Bancerek
-
Warsaw University, Bialystok
-
Supported by RPBP.III-24.C1.
Summary.
-
The article includes the proof of the contraction lemma
which claims that every class in which the axiom of extensionality
is valid is isomorphic with a transitive class. In this article
the isomorphism (wrt membership relation) of two sets is defined.
It is based on [6].
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[8]
[9]
[4]
[1]
[5]
[3]
[2]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek.
A model of ZF set theory language.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Grzegorz Bancerek.
Models and satisfiability.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Andrzej Mostowski.
\em Constructible Sets with Applications.
North Holland, 1969.
- [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [8]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [9]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received April 14, 1989
[
Download a postscript version,
MML identifier index,
Mizar home page]