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Characteristic properties

Various equivalent formulations to the above definition exist. For example, L is distributive if and only if the following holds for all elements x, y, z in L:

Similarly, L is distributive if and only if

: and always imply

The simplest non-distributive lattices are M₃, the "diamond lattice", and N₅, the "pentagon lattice". A lattice is distributive if and only if none of its sublattices is isomorphic to M₃ or N₅;

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