Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Variables in Formulae of the First Order Language

Czeslaw Bylinski

Warsaw University, Bialystok

Grzegorz Bancerek

Warsaw University, Bialystok
Summary.

We develop the first order language defined in [6].
We continue the work done in the article [1].
We prove some schemes of defining by structural induction.
We deal with notions of closed subformulae and of still not bound variables
in a formula. We introduce the concept of the set of all free variables
and the set of all fixed variables occurring in a formula.
Partially supported by RPBP.III24.C1.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[5]
[9]
[8]
[3]
[4]
[2]
[6]
[1]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
Connectives and subformulae of the first order language.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Piotr Rudnicki and Andrzej Trybulec.
A first order language.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [9]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received November 23, 1989
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