Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996
Association of Mizar Users
Adjacency Concept for Pairs of Natural Numbers

Yatsuka Nakamura

Shinshu University, Nagano

Andrzej Trybulec

Warsaw University, Bialystok
Summary.

First, we introduce the concept of adjacency for a pair of natural numbers.
Second, we extend the concept for two pairs of natural numbers. The pairs
represent points of a lattice in a plane.
We show that if some property is infectious among adjacent points,
and some points have the property, then all points have the property.
MML Identifier:
GOBRD10
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[4]
[12]
[10]
[1]
[7]
[13]
[3]
[2]
[5]
[11]
[6]
[8]
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.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a nonempty sets.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Katarzyna Jankowska.
Matrices. Abelian group of matrices.
Journal of Formalized Mathematics,
3, 1991.
 [7]
Takaya Nishiyama and Yasuho Mizuhara.
Binary arithmetics.
Journal of Formalized Mathematics,
5, 1993.
 [8]
Andrzej Trybulec.
Binary operations applied to functions.
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]
Wojciech A. Trybulec.
Pigeon hole principle.
Journal of Formalized Mathematics,
2, 1990.
 [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received June 10, 1996
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