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.III24.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]