Finite Join and Finite Meet, and Dual Lattices

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

Finite Join and Finite Meet, and Dual Lattices

Andrzej Trybulec: Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

Summary.

The concepts of finite join and finite meet in a lattice are introduced. Some properties of the finite join are proved. After introducing the concept of dual lattice in view of dualism we obtain analogous properties of the meet. We prove these properties of binary operations in a lattice, which are usually included in axioms of the lattice theory. We also introduce the concept of Heyting lattice (a bounded lattice with relative pseudo-complements).

MML Identifier: LATTICE2

The terminology and notation used in this paper have been introduced in the following articles [10] [13] [14] [3] [4] [6] [5] [8] [2] [15] [7] [11] [12] [9] [1]

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. Filters --- part I. Journal of Formalized Mathematics, 2, 1990.

[2] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.

[6] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.

[7] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.

[8] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.

[9] Andrzej Trybulec. Semilattice operations on finite subsets. Journal of Formalized Mathematics, 1, 1989.

[10] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[11] Andrzej Trybulec and Agata Darmochwal. Boolean domains. Journal of Formalized Mathematics, 1, 1989.

[12] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.

[13] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[14] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[15] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received August 10, 1990

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