Journal of Formalized Mathematics
Volume 7, 1995
University of Bialystok
Copyright (c) 1995 Association of Mizar Users

The Subformula Tree of a Formula of the First Order Language


Oleg Okhotnikov
Ural University, Ekaterinburg

Summary.

A continuation of [12]. The notions of list of immediate constituents of a formula and subformula tree of a formula are introduced. The some propositions related to these notions are proved.

MML Identifier: QC_LANG4

The terminology and notation used in this paper have been introduced in the following articles [15] [11] [19] [17] [3] [20] [9] [10] [13] [8] [18] [1] [4] [5] [6] [7] [14] [2] [16]

Contents (PDF format)

  1. Preliminaries
  2. Subformula tree

Acknowledgments

The author wishes to thank to G. Bancerek for his assistance during the preparation of this paper.

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. Connectives and subformulae of the first order language. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek. Introduction to trees. Journal of Formalized Mathematics, 1, 1989.
[5] Grzegorz Bancerek. K\"onig's Lemma. Journal of Formalized Mathematics, 3, 1991.
[6] Grzegorz Bancerek. Joining of decorated trees. Journal of Formalized Mathematics, 5, 1993.
[7] Grzegorz Bancerek. Subtrees. Journal of Formalized Mathematics, 6, 1994.
[8] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[12] Czeslaw Bylinski and Grzegorz Bancerek. Variables in formulae of the first order language. Journal of Formalized Mathematics, 1, 1989.
[13] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[14] Piotr Rudnicki and Andrzej Trybulec. A first order language. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[17] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[18] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received October 2, 1995

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