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  for all x, y, and z in L.

In every lattice, if one defines the order relation p<=q as usual to mean p?q=p, then the inequality x ? (y ? z) >= (x ? y) ? (x ? z) and its dual x ? (y ? z) <= (x ? y) ? (x ? z) are always true. A lattice is distributive if one of the converse inequalities holds, too.More information on the relationship of this condition to other distributivity conditions of order theory can be found in the article Distributivity (order theory).

Sholander

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