Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Pigeon Hole Principle

Wojciech A. Trybulec

Warsaw University
Summary.

We introduce the notion of a predicate that states that a function
is onetoone at a given element of its domain (i.e. counterimage of image
of the element is equal to its singleton).
We also introduce some rather technical functors concerning finite sequences:
the lowest index of the given element of the range of the finite sequence,
the substring preceding (and succeeding) the first occurrence of given
element of the range.
At the end of the article we prove the pigeon hole principle.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[10]
[8]
[3]
[11]
[4]
[1]
[5]
[6]
[2]
[9]
Contents (PDF format)
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 and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
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]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [9]
Wojciech A. Trybulec.
Noncontiguous substrings and onetoone finite sequences.
Journal of Formalized Mathematics,
2, 1990.
 [10]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received April 8, 1990
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