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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

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Volume 22, Issue 1


Definition of Flat Poset and Existence Theorems for Recursive Call

Kazuhisa Ishida / Yasunari Shidama / Adam Grabowski
Published Online: 2014-03-30 | DOI: https://doi.org/10.2478/forma-2014-0001


This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this we extensively use technical Mizar functors like BaseFunc or RecFunc. The remaining part builds the background for information engineering approach for lists, namely recursive call for posets [21].We formalized some facts from Chapter 8 of this book as an introduction to the next two sections where we concentrate on binary product of posets rather than on a more general case.

Keywords: flat posets; recursive calls for posets; flattening operator


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About the article

Published Online: 2014-03-30

Citation Information: Formalized Mathematics, Volume 22, Issue 1, Pages 1–10, ISSN (Online) 1898-9934, DOI: https://doi.org/10.2478/forma-2014-0001.

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© by Kazuhisa Ishida. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0) BY-SA 3.0

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