Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Segments of Natural Numbers and Finite Sequences
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Grzegorz Bancerek
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Warsaw University, Bialystok
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Krzysztof Hryniewiecki
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Warsaw University, Warsaw
Summary.
-
We define the notion of an initial segment of natural numbers and prove
a number of their properties.
Using this notion we introduce finite sequences, subsequences,
the empty sequence, a sequence of a domain, and the operation
of concatenation of two sequences.
Supported by RPBP.III-24.C1.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[7]
[11]
[4]
[12]
[6]
[5]
[3]
[2]
[10]
[8]
[1]
-
Main Part
-
Moved from \cite{FINSET_1.ABS}, 1998
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Moved from \cite{CARD_1.ABS}, 1999
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.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Grzegorz Bancerek.
Sequences of ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Grzegorz Bancerek.
Zermelo theorem and axiom of choice.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Czeslaw Bylinski.
Functions and their basic properties.
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.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [10]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [11]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [12]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received April 1, 1989
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