Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993
Association of Mizar Users
Joining of Decorated Trees
-
Grzegorz Bancerek
-
Polish Academy of Sciences, Institute of Mathematics, Warsaw
Summary.
-
This is the continuation of the sequence of articles on trees
(see [2], [4], [5]).
The main goal is to introduce joining operations
on decorated trees corresponding with operations
introduced in [5].
We will also introduce the operation of substitution.
In the last section we dealt with trees decorated by Cartesian
product, i.e. we showed some lemmas on joining operations applied to
such trees.
MML Identifier:
TREES_4
The terminology and notation used in this paper have been
introduced in the following articles
[13]
[9]
[15]
[14]
[1]
[16]
[8]
[10]
[12]
[11]
[7]
[6]
[2]
[4]
[3]
[5]
-
Joining of Decorated Tree
-
Expanding of Decorated Tree by Substitution
-
Double Decorated Trees
Bibliography
- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Grzegorz Bancerek.
Introduction to trees.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Grzegorz Bancerek.
Cartesian product of functions.
Journal of Formalized Mathematics,
3, 1991.
- [4]
Grzegorz Bancerek.
K\"onig's Lemma.
Journal of Formalized Mathematics,
3, 1991.
- [5]
Grzegorz Bancerek.
Sets and functions of trees and joining operations of trees.
Journal of Formalized Mathematics,
4, 1992.
- [6]
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Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
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Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
- [10]
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Journal of Formalized Mathematics,
1, 1989.
- [11]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
- [12]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
- [13]
Andrzej Trybulec.
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Journal of Formalized Mathematics,
Axiomatics, 1989.
- [14]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [15]
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Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [16]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received October 8, 1993
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