Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Semigroup Operations on Finite Subsets

Czeslaw Bylinski

Warsaw University, Bialystok

Supported by RPBP.III24.C1.
Summary.

A continuation of [10].
The propositions and theorems proved in [10] are extended to
finite sequences. Several additional theorems related to semigroup
operations of functions not included in [10] are proved.
The special notation for operations on finite sequences is introduced.
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[15]
[12]
[1]
[16]
[17]
[4]
[2]
[13]
[6]
[5]
[3]
[9]
[10]
[8]
[7]
[14]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Binary operations applied to finite sequences.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a nonempty sets.
Journal of Formalized Mathematics,
2, 1990.
 [9]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Semilattice operations on finite subsets.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [13]
Andrzej Trybulec and Agata Darmochwal.
Boolean domains.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Wojciech A. Trybulec.
Binary operations on finite sequences.
Journal of Formalized Mathematics,
2, 1990.
 [15]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [16]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [17]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received May 4, 1990
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