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difference of lattice elements

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Definition
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How to prove the following theorem (or something similar):

If our lattice is distributive, then exist no more than one difference of given two elements.

There exists an similar theorem saying that for distributive lattice there exists no more than one complement of given element, but I need the more general case of difference instead of complement.

See also:
http://planetmath.org/encyclopedia/ComplementedLattice.html
--
Victor Porton - http://www.mathematics21.org
* Algebraic General Topology and Math Synthesis
* Category Theory - new concepts

How would you define the difference of two elements in a distributive lattice?

Never mind, I just saw it.

I have provided a proof of this in your entry. Please take a look.

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