The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice.As a preliminary work, we present the proofs of the dependence of other axiomatizations of ortholattices. The formalization of the properties of orthomodular lattices follows [4].
@article{bwmeta1.element.doi-10_2478_v10037-008-0033-z,
author = {El\.zbieta M\k adra and Adam Grabowski},
title = {Orthomodular Lattices},
journal = {Formalized Mathematics},
volume = {16},
year = {2008},
pages = {277-282},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0033-z}
}
Elżbieta Mądra; Adam Grabowski. Orthomodular Lattices. Formalized Mathematics, Tome 16 (2008) pp. 277-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0033-z/
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