Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Definable Functions

Grzegorz Bancerek

Warsaw University, Bialystok
Summary.

The article is continuation of [4] and [3].
It deals with concepts of variables occurring in a formula and free variables,
replacing of variables in a formula and definable functions.
The goal of it is to create a base of facts which are neccesary to show
that every model of ZF set theory is a good model, i.e. it is closed with
respect to fundamental settheoretical operations
(union, intersection, Cartesian product etc.).
The base includes the facts concerning with
the composition and conditional sum of two definable functions.
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[9]
[11]
[12]
[5]
[8]
[7]
[6]
[1]
[2]
[3]
[4]
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.
Properties of ZF models.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Grzegorz Bancerek.
Replacing of variables in formulas of ZF theory.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Trybulec.
Enumerated sets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [11]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received September 26, 1990
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