Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Segments of Natural Numbers and Finite Sequences

Grzegorz Bancerek

Warsaw University, Bialystok

Krzysztof Hryniewiecki

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.III24.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

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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