Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

Subtrees


Grzegorz Bancerek
Institute of Mathematics, Polish Academy of Sciences

Summary.

The concepts of root tree, the set of successors of a node in decorated tree and sets of subtrees are introduced.

This article has been worked out during the visit of the author in Nagano in Summer 1994.

MML Identifier: TREES_9

The terminology and notation used in this paper have been introduced in the following articles [15] [12] [17] [16] [2] [18] [10] [11] [8] [14] [13] [4] [1] [3] [5] [6] [7] [9]

Contents (PDF format)

  1. Root Tree and Successors of Node in Decorated Tree
  2. Set of Subtrees of Decorated Tree
  3. Set of Subtrees of Set of Decorated Tree

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. Introduction to trees. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek. Cartesian product of functions. Journal of Formalized Mathematics, 3, 1991.
[5] Grzegorz Bancerek. K\"onig's Lemma. Journal of Formalized Mathematics, 3, 1991.
[6] Grzegorz Bancerek. Sets and functions of trees and joining operations of trees. Journal of Formalized Mathematics, 4, 1992.
[7] Grzegorz Bancerek. Joining of decorated trees. Journal of Formalized Mathematics, 5, 1993.
[8] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[9] Grzegorz Bancerek and Piotr Rudnicki. On defining functions on trees. Journal of Formalized Mathematics, 5, 1993.
[10] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[12] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[13] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[14] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[17] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[18] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received November 25, 1994

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