Tim's Rudimentary
Treadle Reducer

The Idea of Tekla's Proof

Like many things in mathematics, once you know the theorem, the proof isn't hard. The idea is this: suppose we have a solution to the problem, and that S is one of the sets in our solution. Suppose, further, that S is used either alone or in combination to form the targets T1, T2, T3, ... Tn. Then you will still have a solution if you replace the set S with the intersection of the targets T1, T2, T3, ... Tn. Do this with every set in the solution, and you have a solution made of sets, each of which is an intersection of targets.

That's the idea; I leave you to work out the details.

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Tim McLarnan,
Tremewan Professor of Mathematics
Earlham College,
Richmond, IN 47374 USA

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Page last updated: March 7, 2005