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from Brown Corpus
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The idea of the proof is this.
If the direct-sum decomposition ( A ) is valid, how can we get hold of the projections Af associated with the decomposition??
The projection Af will be the identity on Af and zero on the other Af.
We shall find a polynomial Af such that Af is the identity on Af and is zero on the other Af, and so that Af, etc..

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