Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Replacing of Variables in Formulas of ZF Theory

Grzegorz Bancerek

Warsaw University, Bialystok

Supported by RPBP.III24.C1.
Summary.

Part one is a supplement to papers
[1], [2], and [3].
It deals with concepts of selector functions,
atomic, negative, conjunctive formulas and etc., subformulas, free
variables, satisfiability and models (it is shown that axioms of the
predicate and the quantifier calculus are satisfied in an arbitrary set).
In part two there are introduced notions of variables occurring
in a formula and replacing of variables in a formula.
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[9]
[7]
[12]
[11]
[13]
[5]
[6]
[4]
[8]
[1]
[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.
Properties of ZF models.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [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.
Some basic properties of sets.
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]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received August 10, 1990
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