Publications/nom-cade-05.ps
author Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1817
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1818
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1819
C007FFC0001FC0001F80001F80003F80003F80003F00003F00007F00007F00007E00007E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1820
0000FE0000FE0000FC0000FC0001FC0001FC0001F80001F80003F80003F80003F00003F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1821
0007F00007F00007E00007E0000FE0000FE0000FC0000FC0001FC0001FC0001F80001F80
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1822
003F80003F80003F00003F00007F00007F00007E0E007E0E00FE0E00FE1E00FC1C00FC1C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1823
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1824
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1825
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1826
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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007E0007F0003F8000FE0007F0003F0000FC0007E0003F0000FC0007E0003F0000FC000F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1828
E0007F0001FC000FE0007E0001F8000FC0007E0001F8000FC000FE0001F8001FC000FC00
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1829
03F8001FC000FC0003F0001F8001FC1C03F0001F8001F81C03F0003F8001F83C07F0003F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1830
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1831
0FC0007E0003E0F00FC0007E0003E0E00FC000FE0003E1C01FC000FE0001E3C01F8000FC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1832
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1833
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1838
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1839
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1844
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1845
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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1FC001F800001F8003F800001F8003F000003F8007E000003FC00FC000003FC00F800000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1850
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1851
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1853
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1863
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1864
>I<0000FE000007FF80000F83C0003E00E0007C00F00078007000F800F001F803F001F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1867
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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1FC0001F80001F80001F80003F80003F00003F00003F00007F00007E007FFFFF7FFFFFFF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1871
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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1C>I<00F800000003FE0001C0078F0003E00E0F8007E01E0F8007E01C0F8007E0380F80
Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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  1878
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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7F003F8007C0F07E003F800780E07E003F000380E0FE003F00038000FC007F00078000FC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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FC000E0003F000FC000E0003F000FC001E0007F001FC001C0007E001F8001C0007E001F8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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  1890
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Christian Urban <urbanc@in.tum.de>
parents:
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  1891
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Christian Urban <urbanc@in.tum.de>
parents:
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  1892
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1893
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Christian Urban <urbanc@in.tum.de>
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  1894
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1895
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Christian Urban <urbanc@in.tum.de>
parents:
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  1896
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1897
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Christian Urban <urbanc@in.tum.de>
parents:
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  1898
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1899
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1900
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1901
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Christian Urban <urbanc@in.tum.de>
parents:
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  1902
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1903
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Christian Urban <urbanc@in.tum.de>
parents:
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  1904
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Christian Urban <urbanc@in.tum.de>
parents:
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  1905
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Christian Urban <urbanc@in.tum.de>
parents:
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  1906
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Christian Urban <urbanc@in.tum.de>
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  1907
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1908
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Christian Urban <urbanc@in.tum.de>
parents:
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  1909
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1910
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  1911
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Christian Urban <urbanc@in.tum.de>
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  1912
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  1914
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Christian Urban <urbanc@in.tum.de>
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  1915
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Christian Urban <urbanc@in.tum.de>
parents:
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  1916
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Christian Urban <urbanc@in.tum.de>
parents:
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  1917
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1918
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1919
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1920
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Christian Urban <urbanc@in.tum.de>
parents:
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  1921
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Christian Urban <urbanc@in.tum.de>
parents:
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  1922
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Christian Urban <urbanc@in.tum.de>
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  1923
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Christian Urban <urbanc@in.tum.de>
parents:
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  1924
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1925
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1926
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1927
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1928
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1929
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1930
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1931
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1932
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1933
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1934
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1935
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1936
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1937
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1938
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1939
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1940
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1941
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1942
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1943
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1944
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1945
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1946
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1947
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1948
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1949
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1950
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1951
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1952
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1953
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1954
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1955
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1956
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1957
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1958
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1959
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1960
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1961
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1962
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1963
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1964
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1965
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1966
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1967
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1968
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1969
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1970
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1971
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1972
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1973
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1974
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1975
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1976
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1977
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1978
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1979
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1980
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1981
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1982
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1983
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1984
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1985
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1986
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1987
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1988
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1989
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1990
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1991
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1992
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1993
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1994
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1995
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1996
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1997
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1998
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1999
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2000
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2001
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2002
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2003
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2004
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2005
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2006
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2007
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2008
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2009
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2010
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2011
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2012
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2013
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2014
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2015
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2016
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2017
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2018
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2019
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2020
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2021
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2022
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2023
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2024
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2025
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2026
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2027
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2028
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2029
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2030
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2031
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2032
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2033
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2034
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2035
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2036
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2037
0001E0001FFF0000780003C0001FFF0000780003C0001FFF0000780003C0001FFF000078
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2038
0003C0001FFF0000000003C0001FFF0000000007C0001FFF0000000007C0001FFF000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2039
000780001FFF000000000780001FFF000000000F80001FFF000000000F80001FFF000000
Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3046
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3047
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3056
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3063
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3157
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3158
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3161
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3162
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3171
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  4877
b(pap)r(er)f(is)h(organised)f(as)g(follo)n(w:)g(Sec.)i(2)e(reviews)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4878
Fm(\013)p Fx(-equiv)-5 b(alence)36 b(for)g(lam)n(b)r(da-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4879
2276 y(terms.)d(Sec.)g(3)f(giv)n(es)g(a)h(construction)f(of)h(an)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4880
(inductiv)n(e)g(set)g(that)g(is)g(bijectiv)n(e)g(with)h(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4881
2376 y Fm(\013)p Fx(-equated)29 b(lam)n(b)r(da-terms)f(and)h(adapts)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4882
(some)g(notions)h(of)g(the)g(nominal)g(logic)f(w)n(ork)g(for)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4883
2476 y(this)21 b(construction.)e(An)i(induction)g(principle)f(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4884
(this)g(set)h(is)f(deriv)n(ed)f(in)i(Sec.)f(4.)g(Examples)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4885
2575 y(of)26 b(Isab)r(elle/HOL)g(formalisations)e(are)i(giv)n(en)f(in)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4886
(Sec.)g(5.)f(Related)g(w)n(ork)f(is)h(men)n(tioned)h(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4887
2675 y(Sec.)h(6,)f(and)g(Sec.)h(7)f(concludes.)523 2929
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4888
y Fp(2)112 b(Preliminaries)523 3117 y Fx(In)42 b(order)d(to)j(motiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4889
b(ate)41 b(a)g(design)g(c)n(hoice)f(later)h(on,)g(w)n(e)g(b)r(egin)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4890
(with)h(a)f(review)g(of)g Fm(\013)p Fx(-)523 3217 y(equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4891
b(alence)29 b(cast)g(in)h(terms)f(of)h(the)f(nominal)h(logic)e(w)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4892
(ork.)g(The)i(set)f(of)h(lam)n(b)r(da-terms)e(is)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4893
3316 y(inductiv)n(ely)g(de\014ned)g(b)n(y)f(the)h(grammar:)1508
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4894
3485 y Fm(\003)22 b Fx(:)107 b Fm(t)46 b Fx(::=)f Fm(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4895
Fl(j)h Fm(t)23 b(t)46 b Fl(j)g Fm(\025a:t)523 3653 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4896
Fx(where)22 b Fm(a)g Fx(is)g(an)h(atom)f(dra)n(wn)f(from)h(a)g(coun)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4897
(table)g(in\014nite)h(set,)f(whic)n(h)h(will)f(in)h(what)f(follo)n(ws)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4898
523 3752 y(b)r(e)28 b(denoted)g(b)n(y)f Fk(A)17 b Fx(.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4899
3852 y(The)37 b(notion)g(of)g Fm(\013)p Fx(-equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4900
b(alence)37 b(for)f Fm(\003)h Fx(is)h(often)f(de\014ned)h(as)e(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4901
(least)e(congruence)523 3952 y(of)i(the)g(equation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4902
Fm(\025a:t)j Fx(=)1380 3964 y Fj(\013)1466 3952 y Fm(\025b:t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4903
Fx([)p Fm(a)g Fx(:=)g Fm(b)p Fx(])d(in)n(v)n(olving)f(a)h(renaming)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4904
(substitution)h(and)f(a)523 4051 y(side-condition,)g(namely)h(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4905
Fm(b)g Fx(do)r(es)g(not)g(o)r(ccur)f(freely)h(in)g Fm(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4906
Fx(.)h(In)f(the)g(nominal)g(logic)523 4151 y(w)n(ork,)e(ho)n(w)n(ev)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4907
(er,)g(atoms)g(are)h(manipulated)g(not)h(b)n(y)f(renaming)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4908
(substitutions,)i(but)g(b)n(y)523 4251 y(p)r(erm)n(utations|bijectiv)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4909
(e)44 b(mappings)f(from)h(atoms)f(to)h(atoms.)f(While)i(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4910
(utations)523 4350 y(ha)n(v)n(e)30 b(some)g(tec)n(hnical)g(adv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4911
b(an)n(tages,)29 b(for)h(example)g(they)h(preserv)n(e)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4912
Fm(\013)p Fx(-equiv)-5 b(alence)30 b(whic)n(h)523 4450
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4913
y(substitutions)f(do)f(not)h([18],)f(their)g(primary)g(reason)e(in)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4914
(the)g(nominal)f(logic)g(w)n(ork)f(is)i(that)523 4549
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4915
y(one)j(can)g(use)h(them)g(to)f(de\014ne)h(the)g(notion)f(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4916
Fo(supp)l(ort)p Fx(.)h(This)f(notion)h(generalises)d(what)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4917
4649 y(is)38 b(mean)n(t)f(b)n(y)g(the)h(set)g(of)g(free)f(atoms)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4918
(an)h(ob)5 b(ject,)37 b(whic)n(h)h(is)f(usually)g(clear)g(in)h(case)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4919
4749 y(the)29 b(ob)5 b(ject)29 b(is)g(an)g(abstract)f(syn)n(tax)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4920
(tree,)g(but)i(less)e(so)h(if)g(the)g(ob)5 b(ject)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4921
b(is)g(a)f(function.)i(The)523 4848 y(generalisation)i(of)i(\\free)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4922
(atoms")g(to)h(functions,)h(ho)n(w)n(ev)n(er,)d(will)i(pla)n(y)g(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4923
(crucial)h(r^)-42 b(ole)33 b(in)523 4948 y(our)27 b(construction)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4924
(the)h(bijectiv)n(e)g(set.)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4925
%%Page: 3 3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4926
TeXDict begin 3 2 bop Black Black 648 448 a Fx(There)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4927
b(are)g(sev)n(eral)g(w)n(a)n(ys)f(for)i(de\014ning)g(the)h(op)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4928
(eration)e(of)h(a)g(p)r(erm)n(utation)g(acting)f(on)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4929
548 y(a)f(lam)n(b)r(da-term.)g(One)h(w)n(a)n(y)e([18])h(that)h(can)g(b)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4930
r(e)g(easily)f(implemen)n(ted)h(in)g(Isab)r(elle/HOL)f(is)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4931
648 y(to)g(represen)n(t)e(p)r(erm)n(utations)h(as)g(\014nite)h(lists)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4932
(whose)f(elemen)n(ts)g(are)g(sw)n(appings)f(\(i.e.,)i(pairs)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4933
747 y(of)i(atoms\).)g(W)-7 b(e)28 b(write)g(suc)n(h)g(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4934
(utation)f(as)h(\()p Fm(a)2117 759 y Fw(1)2168 747 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4935
Fm(b)2204 759 y Fw(1)2241 747 y Fx(\)\()p Fm(a)2349 759
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4936
y Fw(2)2400 747 y Fm(b)2436 759 y Fw(2)2473 747 y Fx(\))14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4937
b Fl(\001)g(\001)g(\001)g Fx(\()p Fm(a)2706 759 y Fj(n)2765
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4938
747 y Fm(b)2801 759 y Fj(n)2846 747 y Fx(\);)28 b(the)h(empt)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4939
(list)523 847 y([])34 b(stands)e(for)h(the)h(iden)n(tit)n(y)f(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4940
(utation.)h(The)f(p)r(erm)n(utation)g(action,)g(written)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4941
Fm(\031)3247 856 y Fi(\001)3286 847 y Fx(\()p Fl(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4942
Fx(\),)523 946 y(can)27 b(then)h(b)r(e)g(de\014ned)g(on)g(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4943
(da-terms)e(as:)1135 1135 y([])1181 1144 y Fi(\001)1220
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4944
1135 y Fm(a)1287 1088 y Fw(def)1298 1135 y Fx(=)34 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4945
Fm(a)798 1335 y Fx(\()p Fm(a)874 1347 y Fw(1)926 1335
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4946
y Fm(a)970 1347 y Fw(2)1007 1335 y Fx(\))23 b(::)g Fm(\031)1181
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4947
1344 y Fi(\001)1220 1335 y Fm(a)1287 1288 y Fw(def)1298
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4948
1335 y Fx(=)1397 1165 y Fh(8)1397 1240 y(<)1397 1389
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4949
y(:)1482 1235 y Fm(a)1526 1247 y Fw(2)1638 1235 y Fx(if)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4950
Fm(\031)1759 1244 y Fi(\001)1798 1235 y Fm(a)g Fx(=)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4951
Fm(a)1996 1247 y Fw(1)1482 1334 y Fm(a)1526 1346 y Fw(1)1638
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4952
1334 y Fx(if)h Fm(\031)1759 1343 y Fi(\001)1798 1334
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4953
y Fm(a)g Fx(=)f Fm(a)1996 1346 y Fw(2)1482 1434 y Fm(\031)1532
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4954
1443 y Fi(\001)1571 1434 y Fm(a)h Fx(otherwise)2267 1222
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4955
y Fm(\031)2317 1231 y Fi(\001)2356 1222 y Fx(\()p Fm(t)2418
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4956
1234 y Fw(1)2478 1222 y Fm(t)2508 1234 y Fw(2)2546 1222
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4957
y Fx(\))2601 1175 y Fw(def)2612 1222 y Fx(=)34 b(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4958
Fm(\031)2793 1231 y Fi(\001)2832 1222 y Fm(t)2862 1234
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4959
y Fw(1)2922 1222 y Fm(\031)2972 1231 y Fi(\001)3011 1222
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4960
y Fm(t)3041 1234 y Fw(2)3078 1222 y Fx(\))2280 1347 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4961
Fm(\031)2330 1356 y Fi(\001)2368 1347 y Fx(\()p Fm(\025a:t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4962
Fx(\))2601 1300 y Fw(def)2612 1347 y Fx(=)g Fm(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4963
Fx(\()p Fm(\031)2841 1356 y Fi(\001)2880 1347 y Fm(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4964
Fx(\))p Fm(:)p Fx(\()p Fm(\031)3061 1356 y Fi(\001)3100
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4965
1347 y Fm(t)p Fx(\))3332 1272 y(\(1\))523 1620 y(where)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4966
Fm(a)14 b(b)p Fx(\))35 b(::)h Fm(\031)i Fx(is)c(the)i(comp)r(osition)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4967
(of)h(a)f(p)r(erm)n(utation)h(follo)n(w)n(ed)e(b)n(y)i(the)g(sw)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4968
(apping)523 1720 y(\()p Fm(a)14 b(b)p Fx(\).)30 b(The)g(comp)r(osition)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4969
f(of)g Fm(\031)34 b Fx(follo)n(w)n(ed)28 b(b)n(y)i(another)e(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4970
(utation)i Fm(\031)2824 1689 y Fg(0)2877 1720 y Fx(is)g(giv)n(en)f(b)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4971
(y)g(list-)523 1819 y(concatenation,)c(written)i(as)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4972
Fm(\031)1516 1789 y Fg(0)1539 1819 y Fx(@)p Fm(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4973
Fx(,)h(and)f(the)h(in)n(v)n(erse)e(of)h(a)g(p)r(erm)n(utation)g(is)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4974
(giv)n(en)g(b)n(y)g(list)523 1919 y(rev)n(ersal,)f(written)j(as)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4975
Fm(\031)1294 1889 y Fg(\000)p Fw(1)1384 1919 y Fx(.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4976
2019 y(While)i(the)h(represen)n(tation)d(of)i(p)r(erm)n(utations)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4977
(based)f(on)h(lists)g(of)g(sw)n(appings)f(is)h(con-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4978
2119 y(v)n(enien)n(t)f(for)f(de\014nitions)h(lik)n(e)g(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4979
(utation)g(comp)r(osition)f(and)h(the)g(in)n(v)n(erse)f(of)h(a)f(p)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4980
(erm)n(u-)523 2219 y(tation,)32 b(this)g(list-represen)n(tation)e(is)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4981
(not)g(unique;)g(for)f(example)h(the)g(p)r(erm)n(utation)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4982
Fm(a)14 b(a)p Fx(\))523 2318 y(is)24 b(\\equal")f(to)h(the)h(iden)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4983
(tit)n(y)f(p)r(erm)n(utation.)g(Therefore)f(some)h(means)g(to)g(iden)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4984
(tify)h(\\equal")523 2418 y(p)r(erm)n(utations)i(is)h(needed.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4985
Black 523 2596 a Ff(De\014nition)j(1)p Black 41 w(\(Disagreemen)m(t)45
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4986
b(Set)h(and)h(P)m(erm)m(utation)f(Equalit)m(y\).)h Fo(The)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4987
Fx(dis-)523 2696 y(agreemen)n(t)28 b(set)j Fo(of)h(two)g(p)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4988
(ermutations,)g(say)g Fm(\031)2035 2708 y Fw(1)2104 2696
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4989
y Fo(and)f Fm(\031)2313 2708 y Fw(2)2351 2696 y Fo(,)h(is)g(the)f(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4990
(of)h(atoms)g(on)f(which)523 2820 y(the)f(p)l(ermutations)g(disagr)l(e)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4991
l(e,)i(that)e(is)g Fe(ds)o Fx(\()p Fm(\031)1927 2832
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4992
y Fw(1)1965 2820 y Fm(;)14 b(\031)2049 2832 y Fw(2)2086
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4993
2820 y Fx(\))2142 2769 y Fd(def)2154 2820 y Fx(=)35 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4994
Fl(f)23 b Fm(a)g Fl(j)h Fm(\031)2480 2832 y Fw(1)2517
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4995
2829 y Fi(\001)2555 2820 y Fm(a)g Fl(6)p Fx(=)f Fm(\031)2758
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4996
2832 y Fw(2)2795 2829 y Fi(\001)2833 2820 y Fm(a)h Fl(g)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4997
Fo(.)30 b(Two)g(p)l(ermu-)523 2920 y(tations)g(ar)l(e)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4998
b Fx(equal)p Fo(,)30 b(written)f Fm(\031)1525 2932 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4999
Fw(1)1586 2920 y Fl(\030)22 b Fm(\031)1720 2932 y Fw(2)1758
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5000
2920 y Fo(,)30 b(pr)l(ovide)l(d)i Fe(ds)o Fx(\()p Fm(\031)2307
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5001
2932 y Fw(1)2345 2920 y Fm(;)14 b(\031)2429 2932 y Fw(2)2466
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5002
2920 y Fx(\))24 b(=)e Fk(?)p Fo(.)648 3097 y Fx(Using)d(the)i(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5003
(utation)f(action)f(on)h(lam)n(b)r(da-terms,)f Fm(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5004
Fx(-equiv)-5 b(alence)20 b(for)f Fm(\003)h Fx(can)g(b)r(e)g(de-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5005
3197 y(\014ned)26 b(in)g(a)f(syn)n(tax)g(directed)h(fashion)f(using)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5006
(the)g(relations)e(\()p Fl(\000)p Fx(\))9 b Fl(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5007
Fx(\()p Fl(\000)p Fx(\))26 b(and)g(\()p Fl(\000)p Fx(\))d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5008
Fl(62)h Fe(fv)o Fx(\()p Fl(\000)p Fx(\);)523 3297 y(see)j(Fig.)h(1.)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5009
(Because)g(of)g(the)h(\\asymmetric")e(rule)h Fl(\031)2234
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5010
3309 y Fj(\025)p Fw(2)2310 3297 y Fx(,)h(it)g(migh)n(t)g(b)r(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5011
(surprising,)e(but:)p Black 523 3475 a Ff(Prop)s(osition)k(1.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5012
Black 41 w Fl(\031)f Fo(is)h(an)g(e)l(quivalenc)l(e)h(r)l(elation.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5013
3653 y Fx(The)23 b(pro)r(of)g(of)g(this)g(prop)r(osition)f(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5014
(omitted:)h(it)f(can)g(b)r(e)h(found)f(in)g(a)g(more)f(general)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5015
(setting)523 3752 y(in)j([18].)g(\(W)-7 b(e)25 b(also)f(omit)h(a)g(pro)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5016
r(of)f(sho)n(wing)g(that)h Fl(\031)g Fx(and)g(=)2408
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5017
3764 y Fj(\013)2480 3752 y Fx(coincide\).)g(In)g(the)g(follo)n(wing,)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5018
523 3877 y([)p Fm(t)p Fx(])599 3889 y Fj(\013)680 3877
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5019
y Fx(will)34 b(stand)f(for)g(the)h Fm(\013)p Fx(-equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5020
b(alence)34 b(class)e(of)i(the)g(lam)n(b)r(da-term)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5021
Fm(t)p Fx(,)g(that)h(is)g([)p Fm(t)p Fx(])3271 3889 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5022
Fj(\013)3351 3830 y Fw(def)3362 3877 y Fx(=)523 3977
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5023
y Fl(f)23 b Fm(t)618 3947 y Fg(0)664 3977 y Fl(j)g Fm(t)740
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5024
3947 y Fg(0)786 3977 y Fl(\031)g Fm(t)g Fl(g)p Fx(,)k(and)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5025
Fm(\003)1239 3992 y Fj(=)p Fg(\031)1356 3977 y Fx(for)f(the)h(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5026
Fm(\003)f Fx(quotien)n(t)h(b)n(y)f Fl(\031)p Fx(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5027
4246 y Fp(3)112 b(The)38 b(Bijectiv)m(e)d(Set)523 4450
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5028
y Fx(In)25 b(this)f(section,)g(w)n(e)h(will)f(de\014ne)h(a)f(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5029
Fm(\010)p Fx(;)h(inside)g(this)f(set)h(w)n(e)f(will)h(subsequen)n(tly)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5030
(iden)n(tify)523 4549 y(\(inductiv)n(ely\))g(a)g(subset,)g(called)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5031
Fm(\003)1639 4561 y Fj(\013)1686 4549 y Fx(,)h(that)g(is)f(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5032
(bijection)h(with)f Fm(\003)2660 4564 y Fj(=)p Fg(\031)2750
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5033
4549 y Fx(.)f(In)h(order)f(to)g(obtain)523 4649 y(the)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5034
b(bijection,)h Fm(\010)f Fx(needs)g(to)g(b)r(e)h(de\014ned)f(so)f(that)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5035
i(it)f(con)n(tains)f(elemen)n(ts)h(corresp)r(onding,)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5036
4749 y(roughly)i(sp)r(eaking,)g(to)h Fm(\013)p Fx(-equated)g(atoms,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5037
(applications)h(and)f(lam)n(b)r(da-abstractions|)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5038
4848 y(that)26 b(is)g(to)g([)p Fm(a)p Fx(])973 4860 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5039
Fj(\013)1021 4848 y Fx(,)g([)p Fm(t)1123 4860 y Fw(1)1160
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5040
4848 y Fm(t)1190 4860 y Fw(2)1227 4848 y Fx(])1250 4860
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5041
y Fj(\013)1324 4848 y Fx(and)g([)p Fm(\025a:t)p Fx(])1675
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5042
4860 y Fj(\013)1723 4848 y Fx(.)g(Whereas)f(this)h(is)g(straigh)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5043
(tforw)n(ard)d(for)j(atoms)f(and)523 4948 y(applications,)f(the)i(lam)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5044
(b)r(da-abstractions)d(are)h(non-trivial:)g(for)g(them)i(w)n(e)f(shall)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5045
g(use)g(some)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5046
%%Page: 4 4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5047
TeXDict begin 4 3 bop Black Black Black 523 369 2915
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5048
4 v 523 898 4 530 v 560 503 184 4 v 560 557 a Fr(a)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5049
b Fc(\031)g Fr(a)760 517 y Fc(\031)820 525 y Fv(v)m(ar)956
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5050
466 y Fr(t)984 474 y Fv(1)1040 466 y Fc(\031)g Fr(s)1157
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5051
474 y Fv(1)1268 466 y Fr(t)1296 474 y Fv(2)1351 466 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5052
Fc(\031)h Fr(s)1469 474 y Fv(2)p 956 494 547 4 v 1033
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5053
557 a Fr(t)1061 565 y Fv(1)1108 557 y Fr(t)1136 565 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5054
Fv(2)1192 557 y Fc(\031)f Fr(s)1309 565 y Fv(1)1356 557
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5055
y Fr(s)1392 565 y Fv(2)1519 504 y Fc(\031)1579 512 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5056
Fv(app)1836 468 y Fr(t)h Fc(\031)f Fr(s)p 1730 488 380
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5057
4 v 1730 557 a(\025a:t)g Fc(\031)g Fr(\025a:s)2125 502
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5058
y Fc(\031)2185 511 y Fn(\025)p Fv(1)2305 450 y Fr(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5059
Fc(6)p Fu(=)g Fr(b)64 b(t)21 b Fc(\031)g Fu(\()p Fr(a)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5060
b(b)p Fu(\))2822 459 y Fi(\001)2860 450 y Fr(s)64 b(a)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5061
b Fc(62)g Ft(fv)o Fu(\()p Fr(s)p Fu(\))p 2305 488 938
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5062
4 v 2588 557 a Fr(\025a:t)21 b Fc(\031)g Fr(\025b:s)3258
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5063
502 y Fc(\031)3318 511 y Fn(\025)p Fv(2)619 739 y Fr(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5064
Fc(6)p Fu(=)g Fr(b)p 567 773 281 4 v 567 846 a(a)9 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5065
Fc(62)g Ft(fv)o Fu(\()p Fr(b)p Fu(\))863 792 y Ft(fv)941
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5066
800 y Fv(v)m(ar)1111 735 y Fr(a)g Fc(62)g Ft(fv)o Fu(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5067
Fr(t)1356 743 y Fv(1)1390 735 y Fu(\))64 b Fr(a)9 b Fc(62)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5068
Ft(fv)p Fu(\()p Fr(t)1730 743 y Fv(2)1764 735 y Fu(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5069
1111 773 683 4 v 1260 846 a Fr(a)g Fc(62)g Ft(fv)o Fu(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5070
Fr(t)1505 854 y Fv(1)1552 846 y Fr(t)1580 854 y Fv(2)1615
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5071
846 y Fu(\))1810 787 y Ft(fv)1888 795 y Fv(app)p 2072
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5072
773 382 4 v 2072 846 a Fr(a)g Fc(62)g Ft(fv)p Fu(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5073
Fr(\025a:t)p Fu(\))2470 792 y Ft(fv)2548 800 y Fn(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5074
Fv(1)2702 735 y Fr(a)21 b Fc(6)p Fu(=)g Fr(b)64 b(a)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5075
b Fc(62)g Ft(fv)o Fu(\()p Fr(t)p Fu(\))p 2702 773 515
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5076
4 v 2772 846 a Fr(a)g Fc(62)g Ft(fv)p Fu(\()p Fr(\025b:t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5077
Fu(\))3233 792 y Ft(fv)3311 800 y Fn(\025)p Fv(2)p 3435
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5078
898 4 530 v 523 901 2915 4 v Black 976 1049 a Fs(Fig.)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5079
b(1.)26 b Fu(Inductiv)n(e)e(de\014nitions)i(for)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5080
Fc(\000)p Fu(\))21 b Fc(\031)g Fu(\()p Fc(\000)p Fu(\))k(and)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5081
Fc(\000)p Fu(\))9 b Fc(62)g Ft(fv)o Fu(\()p Fc(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5082
Fu(\).)p Black Black 523 1332 a Fo(sp)l(e)l(ci\014c)41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5083
b Fx(\\partial")34 b(functions)i(from)g Fk(A)59 b Fx(to)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5084
b Fm(\010)i Fx(\(b)n(y)f(\\partial")e(w)n(e)h(mean)h(functions)g(that)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5085
523 1432 y(return)27 b(\\error")e(for)i(unde\014ned)h(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5086
b(alues)1789 1402 y Fw(1)1826 1432 y Fx(\).)28 b(Th)n(us)f(the)h(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5087
Fm(\010)g Fx(is)f(de\014ned)h(b)n(y)g(the)g(grammar)1206
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5088
1605 y Fm(\010)c Fx(:)106 b Fm(t)46 b Fx(::=)g Fe(er)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5089
Fl(j)h Fe(am)p Fx(\()p Fm(a)p Fx(\))g Fl(j)g Fe(pr)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5090
Fx(\()p Fm(t;)14 b(t)p Fx(\))46 b Fl(j)g Fe(se)o Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5091
Fo(fn)7 b Fx(\))523 1779 y(where)31 b Fe(er)f Fx(stands)g(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5092
(\\error",)d Fm(a)j Fx(for)f(atoms)h(and)g Fo(fn)37 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5093
Fx(stands)31 b(for)f(functions)i(from)e Fk(A)54 b Fx(to)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5094
1879 y Fm(\010)p Fx(.)601 1849 y Fw(2)666 1879 y Fx(This)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5095
b(grammar)e(corresp)r(onds)g(to)i(the)h(inductiv)n(e)f(datat)n(yp)r(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5096
(that)g(one)g(migh)n(t)g(declare)523 1978 y(in)h(Isab)r(elle/HOL)e(as:)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5097
p Black Black 1328 2151 a Fe(datatype)40 b(phi)22 b(=)g(er)1884
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5098
2251 y Fl(j)33 b Fe(am)43 b("atom")1884 2350 y Fl(j)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5099
b Fe(pr)43 b("phi)14 b Fl(\002)g Fe(phi")1884 2450 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5100
Fl(j)33 b Fe(se)43 b("atom)f Fl(\))h Fe(phi")523 2620
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5101
y Fx(where)28 b(it)h(is)g(presupp)r(osed)f(that)h(the)g(t)n(yp)r(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5102
Fe(atom)e Fx(has)h(b)r(een)h(declared.)f(The)h(constructors)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5103
2719 y Fe(am)o Fx(,)f Fe(pr)g Fx(and)g Fe(se)f Fx(will)h(b)r(e)h(used)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5104
(in)g Fm(\003)1670 2731 y Fj(\013)1745 2719 y Fx(for)g(represen)n(ting)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5105
f Fm(\013)p Fx(-equated)h(atoms,)f(applications)523 2819
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5106
y(and)j(lam)n(b)r(da-abstractions.)d(Before)i(the)h(subset)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5107
Fm(\003)2196 2831 y Fj(\013)2273 2819 y Fx(can)g(b)r(e)g(carv)n(ed)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5108
(out)i(from)g Fm(\010)p Fx(,)g(ho)n(w-)523 2919 y(ev)n(er,)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5109
b(some)h(terminology)e(from)i(the)h(nominal)f(logic)f(w)n(ork)g(needs)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5110
(to)g(b)r(e)g(adapted.)g(F)-7 b(or)22 b(this)523 3018
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5111
y(w)n(e)f(o)n(v)n(erload)e(the)i(notion)g(of)g(p)r(erm)n(utation)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5112
(action,)g(that)h(is)f Fm(\031)2475 3027 y Fi(\001)2513
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5113
3018 y Fx(\()p Fl(\000)p Fx(\),)h(and)f(de\014ne)g(abstractly)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5114
3118 y(sets)27 b(that)h(come)f(with)i(a)e(notion)g(of)h(p)r(erm)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5115
(utation:)p Black 523 3283 a Ff(De\014nition)j(2)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5116
41 w(\(PSets\).)41 b Fo(A)c(set)g Fm(X)44 b Fo(e)l(quipp)l(e)l(d)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5117
b(with)g(a)g(p)l(ermutation)f(action)i Fm(\031)3174 3292
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5118
y Fi(\001)3212 3283 y Fx(\()p Fl(\000)p Fx(\))f Fo(is)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5119
3383 y(said)32 b(to)f(b)l(e)g(a)37 b Fx(pset)p Fo(,)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5120
b(if)h(for)g(al)t(l)f Fm(x)26 b Fl(2)f Fm(X)7 b Fo(,)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5121
b(the)f(p)l(ermutation)h(action)h(satis\014es)f(the)g(fol)t(lowing)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5122
3482 y(pr)l(op)l(erties:)p Black Black Black 670 3639
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5123
a(\(i\))p Black 42 w Fx([])851 3648 y Fi(\001)890 3639
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5124
y Fm(x)23 b Fx(=)g Fm(x)p Black 645 3737 a Fo(\(ii\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5125
Black 42 w Fm(\031)852 3749 y Fw(1)890 3737 y Fx(@)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5126
Fm(\031)1002 3749 y Fw(2)1039 3746 y Fi(\001)1077 3737
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5127
y Fm(x)h Fx(=)e Fm(\031)1282 3749 y Fw(1)1320 3746 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5128
Fi(\001)1358 3737 y Fx(\()p Fm(\031)1437 3749 y Fw(2)1475
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5129
3746 y Fi(\001)1513 3737 y Fm(x)p Fx(\))p Black 619 3835
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5130
a Fo(\(iii\))p Black 43 w(if)31 b Fm(\031)933 3847 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5131
Fw(1)994 3835 y Fl(\030)22 b Fm(\031)1128 3847 y Fw(2)1195
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5132
3835 y Fo(then)30 b Fm(\031)1427 3847 y Fw(1)1465 3844
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5133
y Fi(\001)1503 3835 y Fm(x)23 b Fx(=)g Fm(\031)1708 3847
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5134
y Fw(2)1746 3844 y Fi(\001)1784 3835 y Fm(x)523 3982
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5135
y Fx(The)h(informal)f(notation)g Fm(x)h Fl(2)f Fo(pset)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5136
Fx(will)g(b)r(e)h(adopted)e(whenev)n(er)g(it)h(needs)g(to)g(b)r(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5137
(indicated)523 4081 y(that)42 b Fm(x)g Fx(comes)e(from)h(a)g(pset.)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5138
(The)f(idea)g(b)r(ehind)i(the)e(p)r(erm)n(utation)g(action,)g(roughly)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5139
523 4181 y(sp)r(eaking,)32 b(is)h(to)f(p)r(erm)n(ute)h(all)f(atoms)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5140
(in)f(a)h(giv)n(en)f(pset-elemen)n(t.)g(F)-7 b(or)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5141
b(lists,)h(tuples)g(and)523 4281 y(sets)27 b(the)h(p)r(erm)n(utation)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5142
(action)f(is)g(therefore)g(de\014ned)h(p)r(oin)n(t-wise:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5143
Black Black 556 4475 a(lists:)258 b Fm(\031)1031 4484
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5144
y Fi(\001)1070 4475 y Fx([])1139 4428 y Fw(def)1150 4475
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5145
y Fx(=)34 b([])793 4600 y Fm(\031)843 4609 y Fi(\001)882
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5146
4600 y Fx(\()p Fm(x)24 b Fx(::)f Fm(t)p Fx(\))1139 4553
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5147
y Fw(def)1150 4600 y Fx(=)34 b(\()p Fm(\031)1331 4609
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5148
y Fi(\001)1370 4600 y Fm(x)p Fx(\))24 b(::)f(\()p Fm(\031)1624
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5149
4609 y Fi(\001)1663 4600 y Fm(t)p Fx(\))1843 4475 y(tuples:)71
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5150
b Fm(\031)2204 4484 y Fi(\001)2243 4475 y Fx(\()p Fm(x)2322
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5151
4487 y Fw(1)2359 4475 y Fm(;)14 b(:)g(:)g(:)g(;)g(x)2591
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5152
4487 y Fj(n)2637 4475 y Fx(\))2692 4428 y Fw(def)2703
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5153
4475 y Fx(=)34 b(\()p Fm(\031)2884 4484 y Fi(\001)2923
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5154
4475 y Fm(x)2970 4487 y Fw(1)3008 4475 y Fm(;)14 b(:)g(:)g(:)f(;)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5155
(\031)3242 4484 y Fi(\001)3281 4475 y Fm(x)3328 4487
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5156
y Fj(n)3373 4475 y Fx(\))1843 4600 y(sets:)504 b Fm(\031)2555
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5157
4609 y Fi(\001)2594 4600 y Fm(X)2692 4553 y Fw(def)2703
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5158
4600 y Fx(=)34 b Fl(f)p Fm(\031)2894 4609 y Fi(\001)2932
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5159
4600 y Fm(x)14 b Fl(j)g Fm(x)24 b Fl(2)f Fm(X)7 b Fl(g)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5160
Black 523 4680 473 4 v 546 4734 a Fv(1)606 4765 y Fu(This)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5161
b(is)h(one)e(w)n(a)n(y)h(of)h(dealing)f(with)g(partial)h(functions)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5162
(in)f(Isab)r(elle.)546 4825 y Fv(2)606 4857 y Fu(Emplo)n(ying)e(\(on)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5163
(the)f(meta-lev)n(el\))g(a)i(lam)n(b)r(da-calculus-lik)n(e)e(notation)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5164
(for)f(writing)h(suc)n(h)e(func-)606 4948 y(tions,)k(one)e(could)h(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5165
(this)f(grammar)g(just)h(as)h(w)n(ell)f(ha)n(v)n(e)f(written)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5166
Fr(\025a:f)34 b Fu(instead)26 b(of)h Fq(fn)5 b Fu(.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5167
Black Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5168
%%Page: 5 5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5169
TeXDict begin 5 4 bop Black Black 523 448 a Fx(The)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5170
b(p)r(erm)n(utation)f(action)g(for)g Fm(\010)h Fx(is)g(de\014ned)g(o)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5171
(v)n(er)d(the)j(structure)f(as)g(follo)n(ws:)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5172
Black 852 644 a Fm(\031)902 653 y Fi(\001)940 644 y Fe(er)1159
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5173
597 y Fw(def)1170 644 y Fx(=)34 b Fe(er)852 769 y Fm(\031)902
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5174
778 y Fi(\001)940 769 y Fe(am)o Fx(\()p Fm(a)p Fx(\))1159
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5175
722 y Fw(def)1170 769 y Fx(=)g Fe(am)o Fx(\()p Fm(\031)1438
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5176
778 y Fi(\001)1477 769 y Fm(a)p Fx(\))1789 644 y Fm(\031)1839
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5177
653 y Fi(\001)1877 644 y Fe(pr)p Fx(\()p Fm(t)2027 656
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5178
y Fw(1)2064 644 y Fm(;)14 b(t)2131 656 y Fw(2)2168 644
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5179
y Fx(\))2224 597 y Fw(def)2235 644 y Fx(=)34 b Fe(pr)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5180
Fx(\()p Fm(\031)2503 653 y Fi(\001)2542 644 y Fm(t)2572
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5181
656 y Fw(1)2609 644 y Fm(;)14 b(\031)2696 653 y Fi(\001)2734
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5182
644 y Fm(t)2764 656 y Fw(2)2802 644 y Fx(\))1789 769
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5183
y Fm(\031)1839 778 y Fi(\001)1877 769 y Fe(se)p Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5184
Fo(fn)6 b Fx(\))2224 722 y Fw(def)2235 769 y Fx(=)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5185
b Fe(se)o Fx(\()p Fm(\025a:\031)2618 778 y Fi(\001)2657
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5186
769 y Fx(\()p Fo(fn)c Fx(\()p Fm(\031)2873 739 y Fg(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5187
Fw(1)2963 778 y Fi(\001)3001 769 y Fm(a)p Fx(\)\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5188
945 y(where)d(a)f(lam)n(b)r(da-term)h(\(on)g(the)h Fo(meta-level)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5189
b Fx(!\))28 b(sp)r(eci\014es)f(ho)n(w)f(the)i(p)r(erm)n(utation)f(acts)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5190
f(on)523 1070 y(the)i(function)g Fo(fn)7 b Fx(,)27 b(namely)h(as)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5191
Fm(\031)1561 1079 y Fi(\001)1599 1070 y Fo(fn)1701 1023
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5192
y Fw(def)1712 1070 y Fx(=)34 b Fm(\025a:\031)1976 1079
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5193
y Fi(\001)2014 1070 y Fx(\()p Fo(fn)c Fx(\()p Fm(\031)2230
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5194
1040 y Fg(\000)p Fw(1)2320 1079 y Fi(\001)2358 1070 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5195
Fm(a)p Fx(\)\).)648 1169 y(When)f(reasoning)e(ab)r(out)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5196
Fm(\003)1558 1181 y Fj(\013)1634 1169 y Fx(it)i(will)f(sa)n(v)n(e)e(us)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5197
h(some)h(w)n(ork,)e(if)i(w)n(e)g(sho)n(w)f(that)h(certain)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5198
1269 y(sets)e(are)g(psets)g(and)h(then)g(sho)n(w)f(prop)r(erties)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5199
(\(abstractly\))h(for)g(pset-elemen)n(ts.)p Black 523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5200
1436 a Ff(Lemma)j(1.)p Black 40 w Fx(The)25 b(follo)n(wing)f(sets)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5201
(are)f(psets:)i Fk(A)17 b Fx(,)31 b Fm(\003)p Fx(,)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5202
b Fm(\010)p Fx(,)h(and)g(ev)n(ery)e(set)i(of)f(lists)h(\(similarly)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5203
1535 y(tuples)j(and)f(sets\))h(con)n(taining)f(elemen)n(ts)g(from)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5204
(psets.)p Black 523 1702 a Fo(Pr)l(o)l(of.)p Black 43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5205
w Fx(By)g(routine)h(inductions.)1786 b Fl(u)-55 b(t)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5206
1868 y Fx(The)31 b(most)g(imp)r(ortan)n(t)f(notion)h(of)g(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5207
(pset-elemen)n(t)g(is)f(that)i(of)f(its)g Fo(supp)l(ort)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5208
b Fx(\(a)31 b(set)g(of)523 1968 y(atoms\))c(and)h(deriv)n(ed)e(from)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5209
(this)g(the)g(notion)f(of)g Fo(fr)l(eshness)7 b Fx([6]:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5210
Black 523 2134 a Ff(De\014nition)31 b(3)p Black 41 w(\(Supp)s(ort)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5211
b(and)f(F)-8 b(reshness\).)40 b Fo(Given)f(an)e Fm(x)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5212
Fl(2)g Fo(pset)q(,)g(its)45 b Fx(supp)r(ort)37 b Fo(is)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5213
2234 y(de\014ne)l(d)30 b(as:)904 2204 y Fw(3)1289 2358
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5214
y Fe(supp)n Fx(\()p Fm(x)p Fx(\))1598 2307 y Fd(def)1610
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5215
2358 y Fx(=)35 b Fl(f)p Fm(a)22 b Fl(j)h Fe(inf)o Fl(f)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5216
Fm(b)f Fl(j)h Fx(\()p Fm(a)14 b(b)p Fx(\))2299 2367 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5217
Fi(\001)2337 2358 y Fm(x)24 b Fl(6)p Fx(=)e Fm(x)p Fl(gg)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5218
Fm(:)523 2503 y Fo(A)n(n)i(atom)i Fm(a)f Fo(is)g(said)i(to)e(b)l(e)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5219
b Fx(fresh)26 b Fo(for)h(such)f(an)h Fm(x)p Fo(,)g(written)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5220
Fm(a)e Fx(#)h Fm(x)p Fo(,)j(pr)l(ovide)l(d)h Fm(a)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5221
b Fl(62)g Fe(supp)o Fx(\()p Fm(x)p Fx(\))p Fo(.)523 2669
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5222
y Fx(Note)30 b(that)g(as)f(so)r(on)g(as)h(one)f(\014xes)g(the)i(p)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5223
(erm)n(utation)e(action)h(for)f(elemen)n(ts)h(of)f(a)h(set,)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5224
2769 y(notion)25 b(of)h(supp)r(ort)f(is)g(\014xed)h(as)e(w)n(ell.)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5225
(That)f(means)g(that)h(Def.)g(3)f(de\014nes)h(the)f(supp)r(ort)h(for)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5226
523 2869 y(lists,)k(sets)g(and)g(tuples)g(as)g(long)f(as)g(their)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5227
(elemen)n(ts)g(come)g(from)f(psets.)h(Calculating)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5228
2968 y(supp)r(ort)21 b(for)f(terms)h(in)g Fm(\003)f Fx(is)h(simple:)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5229
Fe(supp)n Fx(\()p Fm(a)p Fx(\))j(=)e Fl(f)p Fm(a)p Fl(g)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5230
Fx(,)e Fe(supp)o Fx(\()p Fm(t)2490 2980 y Fw(1)2550 2968
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5231
y Fm(t)2580 2980 y Fw(2)2618 2968 y Fx(\))j(=)g Fe(supp)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5232
Fx(\()p Fm(t)2997 2980 y Fw(1)3034 2968 y Fx(\))5 b Fl([)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5233
Fe(supp)o Fx(\()p Fm(t)3368 2980 y Fw(2)3406 2968 y Fx(\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5234
3068 y(and)28 b Fe(supp)n Fx(\()p Fm(\025a:t)p Fx(\))d(=)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5235
Fe(supp)o Fx(\()p Fm(t)p Fx(\))c Fl([)g(f)p Fm(a)p Fl(g)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5236
Fx(.)27 b(Because)g(of)h(the)h(functions)f(in)g Fe(se)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5237
Fx(\()p Fo(fn)6 b Fx(\),)29 b(the)f(supp)r(ort)523 3168
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5238
y(for)k(terms)f(in)i Fm(\010)f Fx(is)g(more)f(subtle.)i(Ho)n(w)n(ev)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5239
(er,)d(later)i(on,)f(w)n(e)h(shall)g(see)f(that)i(for)e(terms)h(of)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5240
3267 y(the)h(subset)f Fm(\003)988 3279 y Fj(\013)1067
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5241
3267 y Fx(there)g(is)g(simple)h(structural)e(c)n(haracterisation)e(for)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5242
j(their)g(supp)r(ort,)g(just)523 3367 y(lik)n(e)27 b(for)g(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5243
(da-terms.)648 3466 y(First,)g(some)g(prop)r(erties)g(of)g(supp)r(ort)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5244
(and)f(freshness)g(are)g(established.)p Black 523 3633
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5245
a Ff(Lemma)j(2.)p Black 40 w Fx(F)-7 b(or)27 b(all)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5246
Fm(x)23 b Fl(2)h Fo(pset)p Fx(,)p Black Black Black 676
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5247
3791 a(\(i\))p Black 42 w Fm(\031)855 3800 y Fi(\001)894
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5248
3791 y Fe(supp)n Fx(\()p Fm(x)p Fx(\))g(=)f Fe(supp)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5249
Fx(\()p Fm(\031)1547 3800 y Fi(\001)1586 3791 y Fm(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5250
Fx(\),)28 b(and)p Black 653 3889 a(\(ii\))p Black 42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5251
w Fm(a)23 b Fx(#)h Fm(\031)1015 3898 y Fi(\001)1053 3889
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5252
y Fm(x)51 b Fx(if)28 b(and)g(only)f(if)51 b Fm(\031)1720
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5253
3859 y Fg(\000)p Fw(1)1810 3898 y Fi(\001)1848 3889 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5254
Fm(a)23 b Fx(#)g Fm(x)p Fx(.)p Black 523 4056 a Fo(Pr)l(o)l(of.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5255
Black 43 w Fx(\(i\))28 b(follo)n(ws)f(from)g(the)h(calculation:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5256
Black Black 861 4232 a Fm(\031)911 4241 y Fi(\001)950
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5257
4232 y Fe(supp)n Fx(\()p Fm(x)p Fx(\))1259 4185 y Fw(def)1270
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5258
4232 y Fx(=)34 b Fm(\031)1419 4241 y Fi(\001)1458 4232
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5259
y Fl(f)p Fm(a)14 b Fl(j)g Fe(inf)n Fl(f)p Fm(b)g Fl(j)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5260
Fx(\()p Fm(a)g(b)p Fx(\))2012 4241 y Fi(\001)2049 4232
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5261
y Fm(x)23 b Fl(6)p Fx(=)g Fm(x)p Fl(gg)1259 4311 y Fw(def)1270
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5262
4358 y Fx(=)34 b Fl(f)p Fm(\031)1461 4367 y Fi(\001)1499
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5263
4358 y Fm(a)14 b Fl(j)g Fe(inf)o Fl(f)p Fm(b)g Fl(j)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5264
Fx(\()p Fm(a)g(b)p Fx(\))2012 4367 y Fi(\001)2049 4358
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5265
y Fm(x)23 b Fl(6)p Fx(=)g Fm(x)p Fl(gg)1270 4458 y Fx(=)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5266
b Fl(f)p Fm(\031)1461 4467 y Fi(\001)1499 4458 y Fm(a)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5267
b Fl(j)g Fe(inf)o Fl(f)p Fm(\031)1817 4467 y Fi(\001)1855
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5268
4458 y Fm(b)g Fl(j)g Fx(\()p Fm(a)g(b)p Fx(\))2100 4467
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5269
y Fi(\001)2137 4458 y Fm(x)24 b Fl(6)p Fx(=)e Fm(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5270
Fl(gg)531 b Fx(\()p Fl(\003)3031 4428 y Fw(1)3068 4458
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5271
y Fx(\))1270 4557 y(=)34 b Fl(f)p Fm(a)14 b Fl(j)g Fe(inf)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5272
Fl(f)p Fm(b)g Fl(j)g Fx(\()p Fm(\031)1847 4527 y Fg(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5273
Fw(1)1936 4566 y Fi(\001)1974 4557 y Fm(a)37 b(\031)2105
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5274
4527 y Fg(\000)p Fw(1)2194 4566 y Fi(\001)2232 4557 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5275
Fm(b)p Fx(\))2300 4566 y Fi(\001)2338 4557 y Fm(x)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5276
b Fl(6)p Fx(=)f Fm(x)p Fl(gg)1270 4657 y Fx(=)34 b Fl(f)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5277
Fm(a)14 b Fl(j)g Fe(inf)n Fl(f)p Fm(b)g Fl(j)g Fm(\031)1815
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5278
4666 y Fi(\001)1852 4657 y Fx(\()p Fm(\031)1934 4627
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5279
y Fg(\000)p Fw(1)2024 4666 y Fi(\001)2062 4657 y Fm(a)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5280
b(\031)2193 4627 y Fg(\000)p Fw(1)2283 4666 y Fi(\001)2321
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5281
4657 y Fm(b)p Fx(\))2389 4666 y Fi(\001)2427 4657 y Fm(x)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5282
b Fl(6)p Fx(=)g Fm(\031)2635 4666 y Fi(\001)2674 4657
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5283
y Fm(x)p Fl(gg)152 b Fx(\()p Fl(\003)3031 4627 y Fw(2)3068
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5284
4657 y Fx(\))1270 4783 y(=)34 b Fl(f)p Fm(a)14 b Fl(j)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5285
Fe(inf)n Fl(f)p Fm(b)g Fl(j)g Fx(\()p Fm(a)g(b)p Fx(\))1923
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5286
4792 y Fi(\001)1960 4783 y Fm(\031)2010 4792 y Fi(\001)2049
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5287
4783 y Fm(x)23 b Fl(6)p Fx(=)g Fm(\031)2257 4792 y Fi(\001)2295
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5288
4783 y Fm(x)p Fl(gg)2449 4736 y Fw(def)2460 4783 y Fx(=)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5289
b Fe(supp)n Fx(\()p Fm(\031)2815 4792 y Fi(\001)2854
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5290
4783 y Fm(x)p Fx(\))24 b(\()p Fl(\003)3031 4752 y Fw(3)3068
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5291
4783 y Fx(\))p Black 523 4862 473 4 v 546 4916 a Fv(3)606
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5292
4948 y Fu(The)i(predicate)g Ft(inf)g Fu(will)h(stand)f(for)g(a)g(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5293
(b)r(eing)g(in\014nite.)p Black Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5294
%%Page: 6 6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5295
TeXDict begin 6 5 bop Black Black 523 448 a Fx(where)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5296
b(\()p Fl(\003)833 418 y Fw(1)870 448 y Fx(\))i(holds)e(b)r(ecause)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5297
(the)g(sets)g Fl(f)p Fm(b)p Fl(j)14 b Fm(:)g(:)g(:)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5298
Fl(g)23 b Fx(and)h Fl(f)p Fm(\031)2268 457 y Fi(\001)2306
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5299
448 y Fm(b)p Fl(j)14 b Fm(:)g(:)g(:)o Fl(g)24 b Fx(ha)n(v)n(e)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5300
(same)f(n)n(um)n(b)r(er)h(of)523 548 y(elemen)n(ts,)f(and)f(where)h(\()
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5301
p Fl(\003)1347 518 y Fw(2)1384 548 y Fx(\))g(holds)f(b)r(ecause)g(p)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5302
(erm)n(utations)h(preserv)n(e)e(\(in\)equalities;)i(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5303
Fl(\003)3369 518 y Fw(3)3406 548 y Fx(\))523 648 y(holds)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5304
b(b)r(ecause)g Fm(\031)j Fx(comm)n(utes)d(with)h(the)g(sw)n(apping,)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5305
(that)h(is)g Fm(\031)s Fx(@\()p Fm(a)14 b(b)p Fx(\))31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5306
b Fl(\030)f Fx(\()p Fm(\031)3019 657 y Fi(\001)3058 648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5307
y Fm(a)42 b(\031)3194 657 y Fi(\001)3232 648 y Fm(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5308
Fx(\)@)p Fm(\031)s Fx(.)523 747 y(\(ii\):)29 b(F)-7 b(or)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5309
b(all)h Fm(\031)s Fx(,)g Fm(a)24 b Fl(2)h Fe(supp)o Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5310
Fm(x)p Fx(\))k(if)h(and)e(only)g(if)h Fm(\031)2067 756
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5311
y Fi(\001)2106 747 y Fm(a)24 b Fl(2)h Fm(\031)2304 756
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5312
y Fi(\001)2343 747 y Fe(supp)n Fx(\()p Fm(x)p Fx(\).)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5313
b(The)f(prop)r(ert)n(y)e(follo)n(ws)523 847 y(then)h(from)f(\(i\))i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5314
(and)e Fm(x)d Fl(2)f Fo(pset)p Fx(.)1884 b Fl(u)-55 b(t)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5315
1008 y Fx(Another)18 b(imp)r(ortan)n(t)g(prop)r(ert)n(y)f(is)h(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5316
(fact)g(that)f(the)h(freshness)f(of)g(t)n(w)n(o)g(atoms)f(w.r.t.)i(an)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5317
523 1107 y(pset-elemen)n(t)27 b(means)g(that)g(a)g(p)r(erm)n(utation)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5318
(sw)n(apping)f(those)g(t)n(w)n(o)h(atoms)f(has)h(no)g(e\013ect:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5319
Black 523 1268 a Ff(Lemma)j(3.)p Black 40 w Fx(F)-7 b(or)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5320
b(all)h Fm(x)23 b Fl(2)h Fo(pset)p Fx(,)j(if)i Fm(a)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5321
b Fx(#)i Fm(x)k Fx(and)f Fm(b)c Fx(#)g Fm(x)28 b Fx(then)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5322
Fm(a)14 b(b)p Fx(\))2628 1277 y Fi(\001)2667 1268 y Fm(x)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5323
b Fx(=)g Fm(x)p Fx(.)p Black 523 1429 a Fo(Pr)l(o)l(of.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5324
Black 43 w Fx(The)34 b(case)g Fm(a)g Fx(=)f Fm(b)h Fx(is)g(clear)f(b)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5325
(y)h(Def.)h(2\()p Fm(i;)14 b(iii)p Fx(\).)33 b(In)h(the)g(other)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5326
(case,)f(the)i(assump-)523 1528 y(tion)42 b(implies)g(that)h(b)r(oth)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5327
Fl(f)p Fm(c)14 b Fl(j)g Fx(\()p Fm(c)g(a)p Fx(\))1696
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5328
1537 y Fi(\001)1734 1528 y Fm(x)48 b Fl(6)p Fx(=)e Fm(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5329
Fl(g)d Fx(and)e Fl(f)p Fm(c)14 b Fl(j)g Fx(\()p Fm(c)g(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5330
Fx(\))2526 1537 y Fi(\001)2564 1528 y Fm(x)47 b Fl(6)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5331
Fx(=)g Fm(x)p Fl(g)42 b Fx(are)g(\014nite,)g(and)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5332
1628 y(therefore)34 b(also)g(their)h(union)g(m)n(ust)h(b)r(e)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5333
(\014nite.)h(Hence)f(the)g(corresp)r(onding)f(co-set,)g(that)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5334
1728 y(is)39 b Fl(f)p Fm(c)14 b Fl(j)g Fx(\()p Fm(c)g(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5335
Fx(\))905 1737 y Fi(\001)943 1728 y Fm(x)43 b Fx(=)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5336
Fm(x)26 b Fl(^)h Fx(\()p Fm(c)14 b(b)p Fx(\))1445 1737
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5337
y Fi(\001)1483 1728 y Fm(x)43 b Fx(=)f Fm(x)p Fl(g)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5338
Fx(,)d(is)g(in\014nite)h(\(recall)f(that)g Fk(A)62 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5339
Fx(is)40 b(in\014nite\).)g(If)f(one)523 1827 y(pic)n(ks)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5340
b(from)g(this)g(co-set)f(one)h(elemen)n(t,)h(whic)n(h)f(is)g(from)g(no)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5341
n(w)g(on)g(denoted)g(b)n(y)g Fm(c)g Fx(and)g(as-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5342
1927 y(sumed)g(to)f(b)r(e)h(di\013eren)n(t)g(from)g Fm(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5343
Fx(and)h Fm(b)p Fx(,)f(one)g(has)g(\()p Fm(c)14 b(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5344
Fx(\))2338 1936 y Fi(\001)2377 1927 y Fm(x)30 b Fx(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5345
Fm(x)i Fx(and)f(\()p Fm(c)14 b(b)p Fx(\))2943 1936 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5346
Fi(\001)2981 1927 y Fm(x)31 b Fx(=)e Fm(x)p Fx(.)j(Th)n(us)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5347
2026 y(\()p Fm(c)14 b(a)p Fx(\))681 2035 y Fi(\001)719
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5348
2026 y Fx(\()p Fm(c)g(b)p Fx(\))869 2035 y Fi(\001)908
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5349
2026 y Fx(\()p Fm(c)g(a)p Fx(\))1066 2035 y Fi(\001)1104
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5350
2026 y Fm(x)24 b Fx(=)f Fm(x)p Fx(.)28 b(The)g(p)r(erm)n(utations)f(\()
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5351
p Fm(c)14 b(a)p Fx(\)\()p Fm(c)g(b)p Fx(\)\()p Fm(c)g(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5352
Fx(\))28 b(and)g(\()p Fm(a)14 b(b)p Fx(\))27 b(are)g(equal,)g(since)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5353
2126 y(they)g(ha)n(v)n(e)f(an)h(empt)n(y)g(disagreemen)n(t)e(set.)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5354
(Therefore,)f(b)n(y)h(using)f(Def.)i(2\()p Fm(ii;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5355
b(iii)p Fx(\),)25 b(one)h(can)523 2226 y(conclude)h(with)h(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5356
Fm(a)14 b(b)p Fx(\))1211 2235 y Fi(\001)1250 2226 y Fm(x)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5357
b Fx(=)g Fm(x)p Fx(.)1905 b Fl(u)-55 b(t)648 2386 y Fx(A)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5358
b(further)g(restriction)f(on)g(psets)h(will)g(\014lter)g(out)g(all)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5359
(psets)g(con)n(taining)f(elemen)n(ts)h(with)523 2486
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5360
y(an)i(in\014nite)i(supp)r(ort.)p Black 523 2647 a Ff(De\014nition)i(4)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5361
p Black 41 w(\(Fs-PSet\).)i Fo(A)e(pset)g Fm(X)37 b Fo(is)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5362
b(said)g(to)f(b)l(e)g(an)37 b Fx(fs-pset)31 b Fo(if)h(every)g(element)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5363
(in)523 2746 y Fm(X)36 b Fo(has)31 b(\014nite)e(supp)l(ort.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5364
Black 523 2907 a Ff(Lemma)h(4.)p Black 40 w Fx(The)c(follo)n(wing)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5365
(sets)h(are)f(fs-psets:)h Fk(A)17 b Fx(,)32 b Fm(\003)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5366
Fx(,)26 b(and)g(ev)n(ery)f(set)h(of)g(lists)g(\(similarly)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5367
3007 y(tuples)i(and)f(\014nite)i(sets\))e(con)n(taining)g(elemen)n(ts)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5368
(from)g(fs-psets.)p Black 523 3168 a Fo(Pr)l(o)l(of.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5369
Black 43 w Fx(The)j(supp)r(ort)f(of)h(an)f(atom)g Fm(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5370
Fx(is)f Fl(f)p Fm(a)p Fl(g)p Fx(.)g(The)h(supp)r(ort)f(of)h(a)f(lam)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5371
(b)r(da-term)g Fm(t)g Fx(is)h(the)523 3267 y(set)f(of)f(atoms)g(o)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5372
(ccurring)g(in)h Fm(t)p Fx(.)f(The)h(supp)r(ort)g(of)f(a)h(list)g(is)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5373
(the)h(union)g(of)g(the)g(supp)r(orts)f(of)523 3367 y(its)d(elemen)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5374
(ts,)g(and)g(th)n(us)g(\014nite)g(for)f(fs-pset-elemen)n(ts)h(\(ditto)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5375
(tuples)g(and)g(\014nite)h(sets\).)83 b Fl(u)-55 b(t)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5376
3528 y Fx(The)34 b(set)g Fm(\010)h Fx(is)f Fo(not)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5377
b Fx(an)34 b(fs-pset,)g(b)r(ecause)g(some)f(functions)i(from)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5378
Fk(A)58 b Fx(to)34 b Fm(\010)g Fx(ha)n(v)n(e)f(an)h(in\014-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5379
3627 y(nite)e(supp)r(ort.)f(Similarly)-7 b(,)30 b(some)h(in\014nite)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5380
(sets)f(ha)n(v)n(e)f(in\014nite)i(supp)r(ort,)f(ev)n(en)g(if)g(all)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5381
(their)523 3727 y(elemen)n(ts)24 b(ha)n(v)n(e)f(\014nite)i(supp)r(ort.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5382
f(On)g(the)g(other)g(hand,)g(the)g(in\014nite)h(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5383
Fk(A)47 b Fx(has)23 b Fo(\014nite)30 b Fx(sup-)523 3827
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5384
y(p)r(ort:)d Fe(supp)o Fx(\()p Fk(A)17 b Fx(\))29 b(=)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5385
b Fk(?)k Fx([6].)g(The)h(main)f(prop)r(ert)n(y)f(of)h(elemen)n(ts)h(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5386
f(fs-psets)g(is)g(that)h(there)f(is)523 3926 y(alw)n(a)n(ys)f(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5387
(fresh)g(atom.)p Black 523 4087 a Ff(Lemma)j(5.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5388
40 w Fx(F)-7 b(or)27 b(all)h Fm(x)23 b Fl(2)h Fo(fs-pset)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5389
Fx(,)k(there)f(exists)g(an)g(atom)h Fm(a)f Fx(suc)n(h)g(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5390
Fm(a)23 b Fx(#)h Fm(x)p Fx(.)p Black 523 4248 a Fo(Pr)l(o)l(of.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5391
Black 43 w Fx(Since)36 b Fk(A)59 b Fx(is)35 b(an)h(in\014nite)g(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5392
(and)g(the)g(supp)r(ort)f(of)h Fm(x)g Fx(is)g(b)n(y)f(assumption)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5393
(\014nite,)523 4347 y(there)27 b(m)n(ust)h(b)r(e)g(an)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5394
Fm(a)c Fl(62)h Fe(supp)n Fx(\()p Fm(x)p Fx(\).)1760 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5395
Fl(u)-55 b(t)648 4508 y Fx(W)-7 b(e)35 b(men)n(tioned)g(earlier)f(that)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5396
h(w)n(e)g(are)f(not)h(going)f(to)g(use)h(all)g(functions)g(from)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5397
Fk(A)58 b Fx(to)523 4608 y Fm(\010)30 b Fx(for)g(represen)n(ting)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5398
Fm(\013)p Fx(-equated)i(lam)n(b)r(da-abstractions,)e(but)i(some)f(sp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5399
(eci\014c)h(functions.)3400 4578 y Fw(4)523 4707 y Fx(The)e(follo)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5400
(wing)e(de\014nition)i(states)f(what)h(prop)r(erties)f(these)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5401
(functions)h(need)g(to)f(satisfy)-7 b(.)p Black 523 4771
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5402
473 4 v 546 4825 a Fv(4)606 4857 y Fu(This)35 b(is)f(in)g(con)n(trast)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5403
(to)f(\\w)n(eak")h(and)f(\\full")h(HO)n(AS)d([15,)15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5404
b(4])34 b(whic)n(h)g(use)g(the)g(full)h(function)606
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5405
4948 y(space)26 b(for)h(represen)n(ting)f(lam)n(b)r(da-abstractions.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5406
Black Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5407
%%Page: 7 7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5408
TeXDict begin 7 6 bop Black Black Black 523 448 a Ff(De\014nition)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5409
b(5)p Black 41 w(\(Nominal)26 b(Abstractions\).)j Fo(A)n(n)d(op)l(er)l
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5410
(ation,)j(written)e Fx([)p Fl(\000)p Fx(])p Fm(:)p Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5411
Fl(\000)p Fx(\))p Fo(,)g(taking)523 548 y(an)h(atom)f(and)i(a)e(pset)q
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5412
(-element)g(is)h(said)g(to)g(b)l(e)g(a)34 b Fx(nominal)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5413
b(abstraction)p Fo(,)h(if)j(it)e(satis\014es)h(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5414
648 y(fol)t(lowing)k(pr)l(op)l(erties)f(\(wher)l(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5415
Fm(a)22 b Fl(6)p Fx(=)h Fm(b)p Fo(\):)p Black Black Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5416
670 807 a(\(i\))p Black 42 w Fm(\031)855 816 y Fi(\001)894
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5417
807 y Fx(\([)p Fm(a)p Fx(])p Fm(:x)p Fx(\))h(=)f([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5418
Fm(\031)1303 816 y Fi(\001)1341 807 y Fm(a)p Fx(])p Fm(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5419
Fx(\()p Fm(\031)1513 816 y Fi(\001)1552 807 y Fm(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5420
Fx(\))p Black 645 905 a Fo(\(ii\))p Black 42 w Fx([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5421
Fm(a)p Fx(])p Fm(:x)965 917 y Fw(1)1026 905 y Fx(=)g([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5422
Fm(b)p Fx(])p Fm(:x)1266 917 y Fw(2)1333 905 y Fo(if)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5423
b(and)f(only)g(if)h(either:)p Black Black 1504 1033 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5424
Fm(a)23 b Fx(=)f Fm(b)c Fl(^)h Fm(x)1833 1045 y Fw(1)1894
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5425
1033 y Fx(=)k Fm(x)2029 1045 y Fw(2)2066 1033 y Fo(,)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5426
b(or)1504 1156 y Fm(a)23 b Fl(6)p Fx(=)f Fm(b)c Fl(^)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5427
Fm(x)1833 1168 y Fw(1)1894 1156 y Fx(=)k(\()p Fm(a)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5428
b(b)p Fx(\))2140 1165 y Fi(\001)2178 1156 y Fm(x)2225
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5429
1168 y Fw(2)2281 1156 y Fl(^)19 b Fm(a)k Fx(#)g Fm(x)2561
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5430
1168 y Fw(2)523 1319 y Fx(The)37 b(\014rst)g(prop)r(ert)n(y)f(states)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5431
(that)h(the)h(p)r(erm)n(utation)f(action)f(needs)h(to)g(comm)n(ute)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5432
(with)523 1419 y(nominal)23 b(abstractions.)e(The)i(second)g(prop)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5433
(ert)n(y)e(ensures)i(that)g(nominal)g(abstractions)e(b)r(e-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5434
1518 y(ha)n(v)n(e,)j(roughly)f(sp)r(eaking,)h(lik)n(e)g(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5435
(da-abstractions.)e(T)-7 b(o)24 b(see)h(this)g(reconsider)e(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5436
(rules)523 1618 y Fl(\031)588 1630 y Fj(\025)p Fw(1)687
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5437
1618 y Fx(and)d Fl(\031)908 1630 y Fj(\025)p Fw(2)1006
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5438
1618 y Fx(giv)n(en)g(in)g(Fig.)h(1,)f(whic)n(h)g(can)g(b)r(e)g(used)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5439
(to)f(decide)g(when)h(t)n(w)n(o)e(lam)n(b)r(da-terms)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5440
1718 y(are)27 b Fm(\013)p Fx(-equiv)-5 b(alen)n(t.)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5441
b(Prop)r(ert)n(y)f(\()p Fm(ii)p Fx(\))i(paraphrases)d(these)j(rules)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5442
(for)g(nominal)h(abstractions.)523 1817 y(The)33 b(similarities,)f(ho)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5443
(w)n(ev)n(er,)f(do)h(not)h(end)g(here:)g(giv)n(en)f(a)g([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5444
Fm(a)p Fx(])p Fm(:x)i Fx(with)f Fm(x)f Fl(2)g Fo(fs-pset)q
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5445
Fx(,)h(then)523 1917 y(freshness)27 b(b)r(eha)n(v)n(es)f(lik)n(e)i(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5446
Fl(\000)p Fx(\))9 b Fl(62)23 b Fe(fv)p Fx(\()p Fl(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5447
Fx(\),)k(as)g(sho)n(wn)g(next:)p Black 523 2085 a Ff(Lemma)j(6.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5448
Black 40 w Fx(Giv)n(en)e Fm(a)23 b Fl(6)p Fx(=)f Fm(b)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5449
b Fx(and)f Fm(x)d Fl(2)k Fo(fs-pset)p Fx(,)g(then)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5450
535 2244 a(\(i\))p Black 42 w Fm(a)23 b Fx(#)g([)p Fm(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5451
Fx(])p Fm(:x)28 b Fx(if)g(and)g(only)f(if)h Fm(a)23 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5452
Fx(#)g Fm(x)p Fx(,)29 b(and)p Black 512 2342 a(\(ii\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5453
Black 42 w Fm(a)23 b Fx(#)g([)p Fm(a)p Fx(])p Fm(:x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5454
Black 523 2510 a Fo(Pr)l(o)l(of.)p Black 43 w Fx(\(i)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5455
Fl(\))p Fx(\):)38 b(Since)f Fm(x)j Fl(2)f Fo(fs-pset)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5456
Fx(,)f Fe(supp)n Fx(\([)p Fm(b)p Fx(])p Fm(:x)p Fx(\))i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5457
Fl(\022)e Fe(supp)o Fx(\()p Fm(x)p Fx(\))25 b Fl([)h(f)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5458
Fm(b)p Fl(g)35 b Fx(and)i(therefore)g(the)523 2610 y(supp)r(ort)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5459
b(of)g([)p Fm(a)p Fx(])p Fm(:x)g Fx(m)n(ust)g(b)r(e)h(\014nite.)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5460
(Hence)g(\()p Fm(a;)14 b(b;)g(x;)g Fx([)p Fm(b)p Fx(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5461
Fm(:x)p Fx(\))32 b(is)e(\014nitely)i(supp)r(orted)f(and)f(b)n(y)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5462
2709 y(Lem.)24 b(5)g(there)f(exists)h(a)g Fm(c)g Fx(with)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5463
Fl(\003)p Fx(\))g Fm(c)f Fx(#)g(\()p Fm(a;)14 b(b;)g(x;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5464
Fx([)p Fm(b)p Fx(])p Fm(:x)p Fx(\).)25 b(Using)f(the)g(assumption)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5465
Fm(a)e Fx(#)i([)p Fm(b)p Fx(])p Fm(:x)523 2809 y Fx(and)h(the)h(fact)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5466
(that)g Fm(c)d Fx(#)g([)p Fm(b)p Fx(])p Fm(:x)j Fx(\(from)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5467
Fl(\003)p Fx(\),)h(Lem.)f(3)g(and)h(Def.)g(5\()p Fm(i)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5468
Fx(\))f(giv)n(e)g([)p Fm(b)p Fx(])p Fm(:x)e Fx(=)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5469
Fm(c)14 b(a)p Fx(\)[)p Fm(b)p Fx(])p Fm(:x)23 b Fx(=)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5470
2909 y([)p Fm(b)p Fx(])p Fm(:)p Fx(\()p Fm(c)14 b(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5471
Fx(\))786 2918 y Fi(\001)824 2909 y Fm(x)p Fx(.)37 b(Hence)g(b)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5472
(Def.)h(5\()p Fm(ii)p Fx(\))e Fm(x)j Fx(=)g(\()p Fm(c)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5473
b(a)p Fx(\))2041 2918 y Fi(\001)2079 2909 y Fm(x)p Fx(.)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5474
b(No)n(w)f Fm(c)h Fx(#)h Fm(x)f Fx(\(from)f Fl(\003)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5475
Fx(\))g(implies)h(that)523 3008 y Fm(c)c Fx(#)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5476
Fm(c)14 b(a)p Fx(\))852 3017 y Fi(\001)891 3008 y Fm(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5477
Fx(;)34 b(and)f(mo)n(ving)g(the)g(p)r(erm)n(utation)h(to)f(the)h(other)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5478
f(side)h(b)n(y)f(Lem.)g(2\(ii\))h(giv)n(es)523 3108 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5479
Fm(a)23 b Fx(#)g Fm(x)p Fx(.)g(\(i)p Fl(\()p Fx(\):)g(F)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5480
b(rom)22 b(\()p Fl(\003)p Fx(\),)h Fm(c)g Fx(#)g([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5481
Fm(b)p Fx(])p Fm(:x)g Fx(and)f(therefore)f(b)n(y)h(Lem.)h(2\(ii\))f(\()
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5482
p Fm(a)14 b(c)p Fx(\))2827 3117 y Fi(\001)2866 3108 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5483
Fm(c)23 b Fx(#)g(\()p Fm(a)14 b(c)p Fx(\))p Fm(:)p Fx(\([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5484
Fm(b)p Fx(])p Fm(:x)p Fx(\),)523 3207 y(whic)n(h)28 b(implies)h(b)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5485
(Def.)h(5\()p Fm(i)p Fx(\))f(that)h Fm(a)24 b Fx(#)g([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5486
Fm(b)p Fx(])p Fm(:)p Fx(\(\()p Fm(a)14 b(c)p Fx(\))2137
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5487
3216 y Fi(\001)2176 3207 y Fm(x)p Fx(\).)29 b(F)-7 b(rom)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5488
b(\()p Fl(\003)p Fx(\))g Fm(c)c Fx(#)h Fm(x)j Fx(holds)g(and)g(from)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5489
3307 y(the)33 b(assumption)f(also)f Fm(a)g Fx(#)g Fm(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5490
Fx(;)i(then)g(Lem.)g(3)e(implies)i(that)g Fm(x)e Fx(=)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5491
Fm(a)14 b(c)p Fx(\))2849 3316 y Fi(\001)2887 3307 y Fm(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5492
Fx(,)33 b(and)f(one)g(can)523 3407 y(conclude)27 b(with)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5493
Fm(a)23 b Fx(#)h([)p Fm(b)p Fx(])p Fm(:x)p Fx(.)523 3506
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5494
y(\(ii\):)29 b(By)e Fm(c)d Fx(#)f Fm(x)29 b Fx(and)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5495
Fm(c)d Fl(6)p Fx(=)f Fm(a)k Fx(\(b)r(oth)i(from)e Fl(\003)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5496
Fx(\))h(w)n(e)g(can)f(use)h(\(i\))g(to)g(infer)g Fm(c)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5497
b Fx(#)h([)p Fm(a)p Fx(])p Fm(:x)p Fx(.)k(F)-7 b(urther,)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5498
3606 y(from)33 b(Lem.)h(2\(ii\))f(it)h(holds)f(that)h(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5499
Fm(c)14 b(a)p Fx(\))1781 3615 y Fi(\001)1819 3606 y Fm(c)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5500
b Fx(#)g(\()p Fm(c)14 b(a)p Fx(\))2148 3615 y Fi(\001)2186
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5501
3606 y Fx([)p Fm(a)p Fx(])p Fm(:x)p Fx(.)34 b(This)f(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5502
Fm(a)e Fx(#)h([)p Fm(c)p Fx(])p Fm(:)p Fx(\()p Fm(c)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5503
b(a)p Fx(\))3129 3615 y Fi(\001)3168 3606 y Fm(x)33 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5504
Fx(using)523 3706 y(Def.)41 b(5\()p Fm(i)p Fx(\).)g(Since)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5505
Fm(c)45 b Fl(6)p Fx(=)f Fm(a)p Fx(,)c Fm(c)k Fx(#)h Fm(x)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5506
Fx(and)f(\()p Fm(c)14 b(a)p Fx(\))2051 3715 y Fi(\001)2090
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5507
3706 y Fm(x)45 b Fx(=)f(\()p Fm(c)14 b(a)p Fx(\))2449
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5508
3715 y Fi(\001)2487 3706 y Fm(x)p Fx(,)41 b(Def.)g(5\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5509
Fm(ii)p Fx(\))f(implies)h(that)523 3805 y([)p Fm(c)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5510
Fx(])p Fm(:)p Fx(\()p Fm(c)14 b(a)p Fx(\))786 3814 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5511
Fi(\001)825 3805 y Fm(x)23 b Fx(=)g([)p Fm(a)p Fx(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5512
Fm(:x)p Fx(.)28 b(Therefore,)e Fm(a)d Fx(#)h([)p Fm(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5513
Fx(])p Fm(:x)p Fx(.)1447 b Fl(u)-55 b(t)648 3973 y Fx(The)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5514
b(functions)g(from)g Fk(A)55 b Fx(to)33 b Fm(\010)f Fx(w)n(e)g(iden)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5515
(tify)h(next)f(satisfy)g(the)h(nominal)e(abstraction)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5516
4073 y(prop)r(erties.)c(Let)h([)p Fm(a)p Fx(])p Fm(:t)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5517
Fx(b)r(e)h(de\014ned)g(as)f(follo)n(ws)775 4274 y([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5518
Fm(a)p Fx(])p Fm(:t)941 4227 y Fw(def)952 4274 y Fx(=)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5519
b Fe(se)o Fx(\()p Fm(\025b:)14 b Fe(if)22 b Fm(a)h Fx(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5520
Fm(b)g Fe(then)e Fm(t)i Fe(else)e(if)i Fm(b)f Fx(#)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5521
Fm(t)f Fe(then)e Fx(\()p Fm(a)14 b(b)p Fx(\))2732 4283
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5522
y Fi(\001)2770 4274 y Fm(t)23 b Fe(else)f(er)o Fx(\))h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5523
Fm(:)146 b Fx(\(2\))523 4450 y(This)25 b(op)r(eration)f(tak)n(es)g(t)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5524
(w)n(o)g(argumen)n(ts:)f(an)i Fm(a)e Fl(2)g Fk(A)48 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5525
Fx(and)25 b(a)g Fm(t)e Fl(2)g Fm(\010)p Fx(.)i(T)-7 b(o)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5526
b(see)f(ho)n(w)h(this)g(op)r(er-)523 4549 y(ation)h(enco)r(des)f(an)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5527
Fm(\013)p Fx(-equiv)-5 b(alence)26 b(class,)f(consider)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5528
Fm(\013)p Fx(-equiv)-5 b(alence)26 b(class)f([)p Fm(\025a:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5529
Fx(\()p Fm(a)f(b)p Fx(\)])3391 4561 y Fj(\013)523 4649
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5530
y Fx(and)35 b(the)g(corresp)r(onding)d Fm(\010)p Fx(-term)j([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5531
Fm(a)p Fx(])p Fm(:)p Fe(pr)o Fx(\()p Fm(a;)14 b(b)p Fx(\))35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5532
b(\(for)g(the)g(momen)n(t)f(w)n(e)h(ignore)e(the)i(term)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5533
4749 y(constructor)c Fe(se)g Fx(and)h(only)g(consider)f(the)i(function)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5534
g(giv)n(en)e(b)n(y)h([)p Fm(a)p Fx(])p Fm(:)p Fe(pr)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5535
Fx(\()p Fm(a;)14 b(b)p Fx(\)\).)33 b(The)f(graph)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5536
4848 y(of)27 b(this)h(function)g(is)f(as)g(follo)n(ws:)f(the)i(atom)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5537
Fm(a)g Fx(is)h(mapp)r(ed)f(to)h Fe(pr)o Fx(\()p Fm(a;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5538
b(b)p Fx(\))27 b(since)g(the)h(\014rst)f Fe(if)o Fx(-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5539
4948 y(condition)e(is)h(true.)f(F)-7 b(or)25 b Fm(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5540
Fx(,)h(the)g(\014rst)f Fe(if)o Fx(-condition)g(ob)n(viously)g(fails,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5541
(but)h(also)f(the)h(second)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5542
%%Page: 8 8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5543
TeXDict begin 8 7 bop Black Black 523 448 a Fx(one)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5544
b(fails,)h(b)r(ecause)f Fm(b)e Fl(2)h Fe(supp)n Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5545
Fe(pr)o Fx(\()p Fm(a;)14 b(b)p Fx(\)\);)32 b(therefore)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5546
Fm(b)g Fx(is)h(mapp)r(ed)f(to)h Fe(er)o Fx(.)g(F)-7 b(or)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5547
b(all)i(other)523 548 y(atoms)d Fm(c)p Fx(,)h(w)n(e)f(ha)n(v)n(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5548
Fm(a)e Fl(6)p Fx(=)f Fm(c)k Fx(and)f Fm(c)e Fx(#)g Fe(pr)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5549
Fx(\()p Fm(a;)14 b(b)p Fx(\);)30 b(so)f(the)h Fm(c)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5550
Fx('s)g(are)f(mapp)r(ed)h(b)n(y)f(the)i(function)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5551
648 y(to)c(\()p Fm(a)14 b(c)p Fx(\))782 657 y Fi(\001)820
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5552
648 y Fe(pr)o Fx(\()p Fm(a;)g(b)p Fx(\),)27 b(whic)n(h)g(is)f(just)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5553
Fe(pr)o Fx(\()p Fm(c;)14 b(b)p Fx(\).)27 b(Clearly)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5554
b(,)26 b(the)h(function)g(returns)f Fe(er)g Fx(whenev)n(er)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5555
747 y(the)k(corresp)r(onding)e(lam)n(b)r(da-term)h(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5556
Fo(not)37 b Fx(in)30 b(the)g Fm(\013)p Fx(-equiv)-5 b(alence)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5557
b(class|in)f(this)h(exam-)523 847 y(ple)f Fm(\025b:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5558
Fx(\()p Fm(b)24 b(b)p Fx(\))g Fl(62)h Fx([)p Fm(\025a:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5559
Fx(\()p Fm(a)g(b)p Fx(\)])1359 859 y Fj(\013)1406 847
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5560
y Fx(;)j(in)h(all)f(other)g(cases,)f(ho)n(w)n(ev)n(er,)f(it)j(returns)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5561
(an)g(appropriately)523 946 y(\\renamed")e(v)n(ersion)g(of)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5562
Fe(pr)o Fx(\()p Fm(a;)14 b(b)p Fx(\).)p Black 523 1167
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5563
a Ff(Lemma)30 b(7.)p Black 40 w Fx(The)e(op)r(eration)f([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5564
Fl(\000)p Fx(])p Fm(:)p Fx(\()p Fl(\000)p Fx(\))g(giv)n(en)g(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5565
Fm(\010)h Fx(in)g(\(2\))g(is)f(a)g(nominal)h(abstraction.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5566
Black 523 1378 a Fo(Pr)l(o)l(of.)p Black 43 w Fx(Def.)h(5\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5567
Fm(i)p Fx(\))e(follo)n(ws)g(from)g(the)h(calculation:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5568
Black Black 643 1571 a Fm(\031)693 1580 y Fi(\001)732
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5569
1571 y Fx([)p Fm(a)p Fx(])p Fm(:t)533 1650 y Fw(def)544
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5570
1697 y Fx(=)34 b Fm(\031)693 1706 y Fi(\001)732 1697
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5571
y Fe(se)o Fx(\()p Fm(\025b:)14 b Fe(if)22 b Fm(a)h Fx(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5572
Fm(b)g Fe(then)e Fm(t)i Fe(else)e(if)i Fm(b)f Fx(#)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5573
Fm(t)f Fe(then)e Fx(\()p Fm(a)14 b(b)p Fx(\))2413 1706
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5574
y Fi(\001)2451 1697 y Fm(t)23 b Fe(else)f(er)o Fx(\))533
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5575
1776 y Fw(def)544 1823 y Fx(=)34 b Fe(se)o Fx(\()p Fm(\025b:)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5576
b(\031)933 1832 y Fi(\001)972 1823 y Fe(if)22 b Fm(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5577
Fx(=)g Fm(\031)1287 1792 y Fg(\000)p Fw(1)1376 1832 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5578
Fi(\001)1415 1823 y Fm(b)f Fe(then)g Fm(t)h Fe(else)e(if)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5579
Fm(\031)2081 1792 y Fg(\000)p Fw(1)2171 1832 y Fi(\001)2209
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5580
1823 y Fm(b)h Fx(#)g Fm(t)g Fe(then)e Fx(\()p Fm(a)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5581
b(\031)2764 1792 y Fg(\000)p Fw(1)2854 1832 y Fi(\001)2892
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5582
1823 y Fm(b)p Fx(\))2960 1832 y Fi(\001)2998 1823 y Fm(t)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5583
b Fe(else)e(er)o Fx(\))544 1922 y(=)34 b Fe(se)o Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5584
Fm(\025b:)14 b Fe(if)23 b Fm(a)g Fx(=)f Fm(\031)1198
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5585
1892 y Fg(\000)p Fw(1)1288 1931 y Fi(\001)1326 1922 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5586
Fm(b)h Fe(then)e Fm(\031)1632 1931 y Fi(\001)1671 1922
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5587
y Fm(t)i Fe(else)e(if)h Fm(b)h Fx(#)g Fm(\031)2232 1931
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5588
y Fi(\001)2271 1922 y Fm(t)g Fe(then)e Fm(\031)2571 1931
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5589
y Fi(\001)2610 1922 y Fx(\()p Fm(a)27 b(\031)2763 1892
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5590
y Fg(\000)p Fw(1)2853 1931 y Fi(\001)2891 1922 y Fm(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5591
Fx(\))2959 1931 y Fi(\001)2997 1922 y Fm(t)c Fe(else)f(er)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5592
Fx(\))i(\()p Fl(\003)p Fx(\))544 2022 y(=)34 b Fe(se)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5593
Fx(\()p Fm(\025b:)14 b Fe(if)23 b Fm(a)g Fx(=)f Fm(\031)1198
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5594
1992 y Fg(\000)p Fw(1)1288 2031 y Fi(\001)1326 2022 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5595
Fm(b)h Fe(then)e Fm(\031)1632 2031 y Fi(\001)1671 2022
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5596
y Fm(t)i Fe(else)e(if)h Fm(b)h Fx(#)g Fm(\031)2232 2031
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5597
y Fi(\001)2271 2022 y Fm(t)g Fe(then)e Fx(\()p Fm(\031)2603
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5598
2031 y Fi(\001)2642 2022 y Fm(a)27 b(b)p Fx(\))2781 2031
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5599
y Fi(\001)2820 2022 y Fm(\031)2870 2031 y Fi(\001)2908
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5600
2022 y Fm(t)c Fe(else)f(er)o Fx(\))544 2121 y(=)34 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5601
Fe(se)o Fx(\()p Fm(\025b:)14 b Fe(if)23 b Fm(\031)1044
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5602
2130 y Fi(\001)1082 2121 y Fm(a)g Fx(=)g Fm(b)g Fe(then)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5603
Fm(\031)1543 2130 y Fi(\001)1581 2121 y Fm(t)j Fe(else)d(if)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5604
Fm(b)h Fx(#)g Fm(\031)2143 2130 y Fi(\001)2182 2121 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5605
Fm(t)g Fe(then)e Fx(\()p Fm(\031)2514 2130 y Fi(\001)2553
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5606
2121 y Fm(a)27 b(b)p Fx(\))2692 2130 y Fi(\001)2730 2121
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5607
y Fm(\031)2780 2130 y Fi(\001)2819 2121 y Fm(t)c Fe(else)e(er)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5608
Fx(\))533 2200 y Fw(def)544 2247 y Fx(=)34 b([)p Fm(\031)716
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5609
2256 y Fi(\001)755 2247 y Fm(a)p Fx(])p Fm(:)p Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5610
Fm(\031)927 2256 y Fi(\001)965 2247 y Fm(t)p Fx(\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5611
2433 y(where)25 b(w)n(e)g(use)g(in)h(\()p Fl(\003)p Fx(\))g(the)g(fact)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5612
f(that)h Fm(\031)1779 2442 y Fi(\001)1817 2433 y Fe(if)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5613
Fm(:::)p Fe(then)n Fm(:::)p Fe(else)o Fm(:::)d Fx(=)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5614
Fe(if)p Fm(:::)p Fe(then)f Fm(\031)2975 2442 y Fi(\001)3014
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5615
2433 y Fm(:::)p Fe(else)g Fm(\031)3330 2442 y Fi(\001)3369
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5616
2433 y Fm(:::)523 2533 y Fx(and)33 b(Lem)f(2\(ii\).)i(In)f(case)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5617
Fm(a)h Fx(=)f Fm(b)p Fx(,)i(Def.)g(5\()p Fm(ii)p Fx(\))g(is)f(b)n(y)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5618
(a)f(simple)h(calculation)f(using)g(exten-)523 2632 y(sionalit)n(y)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5619
(of)g(functions.)h(In)g(case)f Fm(a)d Fl(6)p Fx(=)g Fm(b)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5620
Fx(and)h(Def.)e(5\()p Fm(ii)22 b Fl(\))p Fx(\))q(,)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5621
b(the)h(follo)n(wing)f(form)n(ula)f(can)523 2732 y(b)r(e)g(deriv)n(ed)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5622
(from)g(the)h(assumption)f(b)n(y)g(extensionalit)n(y:)890
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5623
2933 y Fl(8)p Fm(c:)46 b Fe(if)23 b Fm(a)f Fx(=)h Fm(c)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5624
Fe(then)f Fm(t)1594 2945 y Fw(1)1654 2933 y Fe(else)f(if)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5625
Fm(c)h Fx(#)h Fm(t)2143 2945 y Fw(1)2203 2933 y Fe(then)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5626
Fx(\()p Fm(a)14 b(c)p Fx(\))2558 2942 y Fi(\001)2597
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5627
2933 y Fm(t)2627 2945 y Fw(1)2687 2933 y Fe(else)21 b(er)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5628
Fx(=)1042 3033 y Fe(if)g Fm(b)f Fx(=)h Fm(c)g Fe(then)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5629
Fm(t)1585 3045 y Fw(2)1646 3033 y Fe(else)g(if)h Fm(c)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5630
Fx(#)g Fm(t)2134 3045 y Fw(2)2195 3033 y Fe(then)e Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5631
Fm(b)14 b(c)p Fx(\))2542 3042 y Fi(\001)2580 3033 y Fm(t)2610
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5632
3045 y Fw(2)2671 3033 y Fe(else)21 b(er)523 3239 y Fx(Instan)n(tiating)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5633
27 b(this)h(form)n(ula)f(once)g(with)h Fm(a)f Fx(and)h(once)f(with)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5634
Fm(b)f Fx(yields)h(the)g(t)n(w)n(o)e(equations)1345 3435
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5635
y Fm(t)1375 3447 y Fw(1)1436 3435 y Fx(=)c Fe(if)g Fm(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5636
Fx(#)h Fm(t)1823 3447 y Fw(2)1883 3435 y Fe(then)d Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5637
Fm(b)14 b(a)p Fx(\))2238 3444 y Fi(\001)2276 3435 y Fm(t)2306
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5638
3447 y Fw(2)2367 3435 y Fe(else)21 b(er)1345 3534 y Fm(t)1375
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5639
3546 y Fw(2)1436 3534 y Fx(=)h Fe(if)g Fm(b)h Fx(#)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5640
Fm(t)1814 3546 y Fw(1)1875 3534 y Fe(then)e Fx(\()p Fm(a)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5641
b(b)p Fx(\))2230 3543 y Fi(\001)2268 3534 y Fm(t)2298
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5642
3546 y Fw(1)2359 3534 y Fe(else)21 b(er)523 3741 y Fx(Next,)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5643
b(one)g(distinguishes)f(t)n(w)n(o)g(cases)g(where)g Fm(a)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5644
Fx(#)g Fm(t)2181 3753 y Fw(2)2245 3741 y Fx(and)k Fl(:)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5645
b Fm(a)23 b Fx(#)g Fm(t)2664 3753 y Fw(2)2702 3741 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5646
Fx(,)k(resp)r(ectiv)n(ely)-7 b(.)26 b(In)h(the)523 3840
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5647
y(\014rst)h(case,)g Fm(t)925 3852 y Fw(1)986 3840 y Fx(=)c(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5648
Fm(b)14 b(a)p Fx(\))1233 3849 y Fi(\001)1271 3840 y Fm(t)1301
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5649
3852 y Fw(2)1338 3840 y Fx(,)29 b(whic)n(h)f(b)n(y)g(Lem.)h(1)f(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5650
(Def.)h(2\()p Fm(iii)p Fx(\))e(is)h(equal)g(to)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5651
Fm(a)14 b(b)p Fx(\))3147 3849 y Fi(\001)3186 3840 y Fm(t)3216
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5652
3852 y Fw(2)3253 3840 y Fx(;)28 b(and)523 3940 y(ob)n(viously)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5653
b Fm(a)h Fx(#)h Fm(t)1109 3952 y Fw(2)1181 3940 y Fx(b)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5654
(assumption.)g(In)g(the)h(second)f(case)f Fm(t)2519 3952
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5655
y Fw(1)2591 3940 y Fx(=)h Fe(er)o Fx(.)h(This)f(substituted)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5656
4040 y(in)n(to)k(the)g(second)f(equation)g(giv)n(es)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5657
Fm(t)1726 4052 y Fw(2)1804 4040 y Fx(=)i Fe(if)h Fm(b)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5658
Fx(#)i Fe(er)e(then)g Fx(\()p Fm(a)14 b(b)p Fx(\))2721
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5659
4049 y Fi(\001)2759 4040 y Fe(er)39 b(else)g(er)o Fx(.)f(Since)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5660
4139 y Fe(supp)n Fx(\()p Fe(er)p Fx(\))23 b(=)g Fk(?)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5661
Fx(,)g Fm(t)1101 4151 y Fw(2)1162 4139 y Fx(=)f(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5662
Fm(a)14 b(b)p Fx(\))1407 4148 y Fi(\001)1445 4139 y Fe(er)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5663
b Fx(=)f Fe(er)o Fx(.)i(No)n(w)g(there)f(is)h(a)f(con)n(tradiction)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5664
(with)j(the)f(assump-)523 4239 y(tion)31 b Fl(:)14 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5665
Fm(a)29 b Fx(#)g Fm(t)967 4251 y Fw(2)1004 4239 y Fx(,)i(b)r(ecause)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5666
Fm(a)15 b Fx(#)g Fe(er)o Fx(.)32 b(Def.)c(5\()p Fm(ii)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5667
b Fl(\()p Fx(\))31 b(for)g Fm(a)e Fl(6)p Fx(=)f Fm(b)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5668
Fx(is)g(b)n(y)g(extensionalit)n(y)f(and)g(a)523 4338
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5669
y(case-analysis.)2374 b Fl(u)-55 b(t)523 4549 y Fx(Note)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5670
b(that,)g(in)g Fo(gener)l(al)p Fx(,)h(one)e(cannot)h(decide)g(whether)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5671
(t)n(w)n(o)g(functions)i(from)e Fk(A)52 b Fx(to)29 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5672
Fm(\010)g Fx(are)523 4649 y(equal;)g(ho)n(w)n(ev)n(er)f(Def.)i(5\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5673
Fm(ii)p Fx(\))f(pro)n(vides)g(means)g(to)g(decide)h(whether)g([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5674
Fm(a)p Fx(])p Fm(:t)2869 4661 y Fw(1)2932 4649 y Fx(=)d([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5675
Fm(b)p Fx(])p Fm(:t)3159 4661 y Fw(2)3225 4649 y Fx(holds:)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5676
4749 y(one)h(just)g(has)g(to)g(consider)f(whether)h Fm(a)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5677
Fx(=)f Fm(b)28 b Fx(and)g(then)h(apply)e(the)i(appropriate)d(prop)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5678
(ert)n(y)523 4848 y(in)40 b(Def.)h(5\()p Fm(ii)p Fx(\)|just)e(lik)n(e)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5679
(deciding)f(the)i Fm(\013)p Fx(-equiv)-5 b(alence)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5680
b(of)h(t)n(w)n(o)f(lam)n(b)r(da-terms)f(using)523 4948
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5681
y(\()p Fl(\000)p Fx(\))9 b Fl(\031)g Fx(\()p Fl(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5682
Fx(\).)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5683
%%Page: 9 9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5684
TeXDict begin 9 8 bop Black Black 648 448 a Fx(No)n(w)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5685
b(ev)n(erything)f(is)i(in)f(place)h(for)f(de\014ning)g(the)h(subset)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5686
Fm(\003)2498 460 y Fj(\013)2545 448 y Fx(.)g(It)g(is)f(de\014ned)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5687
(inductiv)n(ely)523 548 y(b)n(y)j(the)h(rules:)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5688
Black 1054 704 a Fm(a)23 b Fl(2)g Fk(A)p 956 728 403
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5689
4 v 956 806 a Fe(am)o Fx(\()p Fm(a)p Fx(\))g Fl(2)h Fm(\003)1311
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5690
818 y Fj(\013)1598 695 y Fm(t)1628 707 y Fw(1)1688 695
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5691
y Fl(2)g Fm(\003)1825 707 y Fj(\013)1955 695 y Fm(t)1985
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5692
707 y Fw(2)2045 695 y Fl(2)f Fm(\003)2181 707 y Fj(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5693
1598 728 631 4 v 1649 806 a Fe(pr)o Fx(\()p Fm(t)1798
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5694
818 y Fw(1)1835 806 y Fm(;)14 b(t)1902 818 y Fw(2)1939
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5695
806 y Fx(\))24 b Fl(2)f Fm(\003)2131 818 y Fj(\013)2469
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5696
695 y Fm(a)g Fl(2)g Fk(A)106 b Fm(t)23 b Fl(2)h Fm(\003)2947
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5697
707 y Fj(\013)p 2469 728 525 4 v 2556 806 a Fx([)p Fm(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5698
Fx(])p Fm(:t)f Fl(2)h Fm(\003)2859 818 y Fj(\013)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5699
972 y Fx(using)j(in)h(the)g(third)g(inference)f(rule)h(the)g(op)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5700
(eration)e(de\014ned)i(in)g(\(2\).)g(F)-7 b(or)27 b Fm(\003)2964
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5701
984 y Fj(\013)3038 972 y Fx(w)n(e)h(ha)n(v)n(e:)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5702
523 1146 a Ff(Lemma)i(8.)p Black 68 w Fm(\003)1063 1158
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5703
y Fj(\013)1138 1146 y Fx(is:)p Black Black Black 676
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5704
1269 a(\(i\))p Black 42 w(an)e(fs-pset,)f(and)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5705
653 1368 a(\(ii\))p Black 42 w(closed)g(under)h(p)r(erm)n(utations,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5706
(that)h(is)f(if)h Fm(x)c Fl(2)f Fm(\003)2363 1380 y Fj(\013)2438
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5707
1368 y Fx(then)28 b Fm(\031)2677 1377 y Fi(\001)2715
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5708
1368 y Fm(x)c Fl(2)f Fm(\003)2922 1380 y Fj(\013)2969
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5709
1368 y Fx(.)p Black 523 1541 a Fo(Pr)l(o)l(of.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5710
43 w Fx(\(i\):)34 b(The)f(pset-prop)r(erties)e(of)i Fm(\010)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5711
Fx(carry)e(o)n(v)n(er)g(to)i Fm(\003)2430 1553 y Fj(\013)2477
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5712
1541 y Fx(.)g(The)g(fs-pset)g(prop)r(ert)n(y)e(fol-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5713
1641 y(lo)n(ws)g(b)n(y)g(a)g(routine)g(induction)h(on)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5714
(de\014nition)g(of)f Fm(\003)2360 1653 y Fj(\013)2439
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5715
1641 y Fx(using)g(the)h(fact)g(deriv)n(ed)e(from)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5716
1740 y(Lem.)d(6\(i,ii\))g(that)g(for)f Fm(x)d Fl(2)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5717
Fo(fs-pset)q Fx(,)j Fe(supp)o Fx(\([)p Fm(a)p Fx(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5718
Fm(:x)p Fx(\))e(=)f Fe(supp)n Fx(\()p Fm(x)p Fx(\))17
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5719
b Fl(\000)f(f)p Fm(a)p Fl(g)p Fx(.)26 b(\(ii\))h(Routine)g(induc-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5720
1840 y(tion)h(o)n(v)n(er)e(the)h(de\014nition)h(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5721
Fm(\003)1536 1852 y Fj(\013)1583 1840 y Fx(.)1777 b Fl(u)-55
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5722
b(t)523 2013 y Fx(T)-7 b(aking)31 b(Lem.)h(8\(i\))g(and)g(Lem.)g(6)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5723
(together)g(giv)n(es)g(us)g(a)h(simple)g(c)n(haracterisation)d(of)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5724
(the)523 2113 y(supp)r(ort)38 b(of)h(elemen)n(ts)f(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5725
Fm(\003)1463 2125 y Fj(\013)1510 2113 y Fx(:)g Fe(supp)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5726
Fx(\()p Fe(am)o Fx(\()p Fm(a)p Fx(\)\))j(=)f Fl(f)p Fm(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5727
Fl(g)p Fx(,)d Fe(supp)n Fx(\()p Fe(pr)p Fx(\()p Fm(t)2698
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5728
2125 y Fw(1)2735 2113 y Fm(;)14 b(t)2802 2125 y Fw(2)2839
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5729
2113 y Fx(\)\))42 b(=)f Fe(supp)n Fx(\()p Fm(t)3287 2125
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5730
y Fw(1)3325 2113 y Fx(\))26 b Fl([)523 2213 y Fe(supp)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5731
Fx(\()p Fm(t)759 2225 y Fw(2)797 2213 y Fx(\))j(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5732
Fe(supp)n Fx(\([)p Fm(a)p Fx(])p Fm(:t)p Fx(\))d(=)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5733
Fe(supp)n Fx(\()p Fm(t)p Fx(\))20 b Fl(\000)f(f)p Fm(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5734
Fl(g)p Fx(.)28 b(In)h(other)f(w)n(ords)f(it)j(coincides)e(with)h(what)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5735
523 2312 y(one)e(usually)g(means)h(b)n(y)f(the)h(free)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5736
b(ariables)26 b(of)i(a)f(lam)n(b)r(da-term.)648 2412
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5737
y(Next,)j(one)f(of)h(the)h(main)f(p)r(oin)n(ts)f(of)h(this)g(pap)r(er:)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5738
g(there)g(is)g(a)f(bijection)h(b)r(et)n(w)n(een)g Fm(\003)3348
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5739
2427 y Fj(=)p Fg(\031)523 2511 y Fx(and)d Fm(\003)742
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5740
2523 y Fj(\013)789 2511 y Fx(.)h(This)g(is)f(sho)n(wn)g(b)n(y)g(using)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5741
(the)g(follo)n(wing)e(mapping)h(from)h Fm(\003)f Fx(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5742
Fm(\003)2973 2523 y Fj(\013)3020 2511 y Fx(:)797 2714
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5743
y Fm(q)s Fx(\()p Fm(a)p Fx(\))969 2666 y Fw(def)980 2714
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5744
y Fx(=)33 b Fe(am)p Fx(\()p Fm(a)p Fx(\))166 b Fm(q)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5745
Fx(\()p Fm(t)1542 2726 y Fw(1)1603 2714 y Fm(t)1633 2726
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5746
y Fw(2)1670 2714 y Fx(\))1725 2666 y Fw(def)1736 2714
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5747
y Fx(=)34 b Fe(pr)o Fx(\()p Fm(q)s Fx(\()p Fm(t)2056
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5748
2726 y Fw(1)2094 2714 y Fx(\))p Fm(;)14 b(q)s Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5749
Fm(t)2265 2726 y Fw(2)2303 2714 y Fx(\)\))166 b Fm(q)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5750
Fx(\()p Fm(\025a:t)p Fx(\))2807 2666 y Fw(def)2818 2714
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5751
y Fx(=)33 b([)p Fm(a)p Fx(])p Fm(:q)s Fx(\()p Fm(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5752
Fx(\))523 2895 y(and)27 b(the)h(follo)n(wing)f(lemma:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5753
Black 523 3068 a Ff(Lemma)j(9.)p Black 40 w Fm(t)1007
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5754
3080 y Fw(1)1068 3068 y Fl(\031)22 b Fm(t)1185 3080 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5755
Fw(2)1250 3068 y Fx(if)28 b(and)g(only)f(if)h Fm(q)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5756
Fx(\()p Fm(t)1848 3080 y Fw(1)1886 3068 y Fx(\))23 b(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5757
Fm(q)s Fx(\()p Fm(t)2131 3080 y Fw(2)2168 3068 y Fx(\).)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5758
Black 523 3242 a Fo(Pr)l(o)l(of.)p Black 43 w Fx(By)k(routine)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5759
(induction)g(o)n(v)n(er)d(de\014nition)j(of)g Fm(\003)2268
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5760
3254 y Fj(\013)2315 3242 y Fx(.)1045 b Fl(u)-55 b(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5761
Black 523 3415 a Ff(Theorem)30 b(1.)p Black 41 w Fx(There)d(is)h(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5762
(bijection)h(b)r(et)n(w)n(een)g Fm(\003)2155 3430 y Fj(=)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5763
Fg(\031)2272 3415 y Fx(and)f Fm(\003)2491 3427 y Fj(\013)2538
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5764
3415 y Fx(.)p Black 523 3588 a Fo(Pr)l(o)l(of.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5765
43 w Fx(The)k(mapping)f Fm(q)k Fx(needs)c(to)g(b)r(e)h(lifted)h(to)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5766
Fm(\013)p Fx(-equiv)-5 b(alence)30 b(classes)f(\(see)i([14]\).)f(F)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5767
b(or)523 3688 y(this)31 b(de\014ne)g Fm(q)971 3658 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5768
Fg(0)995 3688 y Fx(\([)p Fm(t)p Fx(])1103 3700 y Fj(\013)1150
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5769
3688 y Fx(\))h(as)e(follo)n(ws:)g(apply)g Fm(q)k Fx(to)d(ev)n(ery)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5770
(elemen)n(t)h(of)f(the)i(set)e([)p Fm(t)p Fx(])3010 3700
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5771
y Fj(\013)3089 3688 y Fx(and)h(build)523 3787 y(the)d(union)f(of)h(the)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5772
g(results.)f(By)g(Lem.)h(9)f(this)h(m)n(ust)f(yield)h(a)f(singleton)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5773
(set.)g(The)h(result)f(of)523 3887 y Fm(q)563 3857 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5774
Fg(0)586 3887 y Fx(\([)p Fm(t)p Fx(])694 3899 y Fj(\013)742
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5775
3887 y Fx(\))33 b(is)g(then)g(the)g(singleton.)f(Surjectivit)n(y)h(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5776
Fm(q)2209 3857 y Fg(0)2265 3887 y Fx(is)h(sho)n(wn)f(b)n(y)g(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5777
(routine)h(induction)523 3987 y(o)n(v)n(er)26 b(the)j(de\014nition)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5778
(of)g Fm(\003)1367 3999 y Fj(\013)1414 3987 y Fx(.)h(Injectivit)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5779
(of)g Fm(q)2000 3957 y Fg(0)2052 3987 y Fx(follo)n(ws)f(from)g(Lem.)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5780
(9)e(since)h([)p Fm(t)3057 3999 y Fw(1)3095 3987 y Fx(])3118
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5781
3999 y Fj(\013)3189 3987 y Fx(=)23 b([)p Fm(t)3330 3999
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5782
y Fw(2)3368 3987 y Fx(])3391 3999 y Fj(\013)523 4086
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5783
y Fx(for)k(all)g Fm(t)795 4098 y Fw(1)856 4086 y Fl(\031)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5784
b Fm(t)973 4098 y Fw(2)1011 4086 y Fx(.)2349 b Fl(u)-55
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5785
b(t)523 4351 y Fp(4)112 b(Structural)36 b(Induction)h(Principle)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5786
4549 y Fx(The)c(de\014nition)h(of)f Fm(\003)1232 4561
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5787
y Fj(\013)1313 4549 y Fx(pro)n(vides)e(an)i(induction)h(principle)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5788
(for)g(free.)g(Ho)n(w)n(ev)n(er,)f(this)h(in-)523 4649
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5789
y(duction)h(principle)f(is)h(not)g(v)n(ery)e(con)n(v)n(enien)n(t)h(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5790
(practice.)f(Consider)f(Fig.)i(2)f(sho)n(wing)f(a)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5791
4749 y(t)n(ypical)k(informal)f(pro)r(of)h(in)n(v)n(olving)e(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5792
(da-terms|it)i(is)g(Barendregt's)e(pro)r(of)i(of)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5793
4848 y(substitution)28 b(lemma)f(tak)n(en)g(from)g([3].)g(This)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5794
(informal)g(pro)r(of)g(considers)f(in)h(the)h(lam)n(b)r(da-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5795
4948 y(case)e(only)g(binders)g Fm(z)j Fx(that)e(ha)n(v)n(e)e(suitable)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5796
(prop)r(erties)e(\(namely)h(b)r(eing)h(fresh)f(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5797
Fm(x)p Fx(,)h Fm(y)s Fx(,)f Fm(N)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5798
%%Page: 10 10
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5799
TeXDict begin 10 9 bop Black Black Black 523 369 2915
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5800
4 v 523 2049 4 1681 v 563 464 a Fs(Substitution)32 b(Lemma:)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5801
b Fu(If)g Fr(x)c Fc(6\021)g Fr(y)28 b Fu(and)e Fr(x)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5802
b Fc(62)i Fr(F)11 b(V)17 b Fu(\()p Fr(L)p Fu(\),)25 b(then)1035
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5803
600 y Fr(M)8 b Fu([)p Fr(x)22 b Fu(:=)f Fr(N)8 b Fu(][)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5804
Fr(y)25 b Fu(:=)d Fr(L)p Fu(])f Fc(\021)h Fr(M)8 b Fu([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5805
Fr(y)24 b Fu(:=)d Fr(L)p Fu(][)p Fr(x)h Fu(:=)g Fr(N)8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5806
b Fu([)p Fr(y)24 b Fu(:=)e Fr(L)p Fu(]].)563 759 y Fs(Pro)r(of:)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5807
b Fu(By)e(induction)h(on)f(the)h(structure)f(of)h Fr(M)8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5808
b Fu(.)563 860 y Fs(Case)29 b(1:)c Fr(M)34 b Fu(is)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5809
b(a)g(v)l(ariable.)681 960 y(Case)h(1.1.)e Fr(M)30 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5810
Fc(\021)21 b Fr(x)p Fu(.)k(Then)h(b)r(oth)f(sides)h(equal)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5811
Fr(N)8 b Fu([)p Fr(y)25 b Fu(:=)c Fr(L)p Fu(])26 b(since)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5812
Fr(x)21 b Fc(6\021)g Fr(y)s Fu(.)681 1061 y(Case)27 b(1.2.)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5813
Fr(M)30 b Fc(\021)21 b Fr(y)s Fu(.)k(Then)h(b)r(oth)f(sides)h(equal)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5814
Fr(L)p Fu(,)g(for)h Fr(x)21 b Fc(62)g Fr(F)11 b(V)17
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5815
b Fu(\()p Fr(L)p Fu(\))25 b(implies)1008 1161 y Fr(L)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5816
Fu([)p Fr(x)c Fu(:=)h Fr(:)13 b(:)g(:)p Fu(])22 b Fc(\021)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5817
Fr(L)p Fu(.)681 1262 y(Case)27 b(1.3.)e Fr(M)30 b Fc(\021)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5818
b Fr(z)j Fc(6\021)d Fr(x;)13 b(y)s Fu(.)25 b(Then)h(b)r(oth)f(sides)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5819
(equal)g Fr(z)s Fu(.)563 1362 y Fs(Case)i(2:)c Fr(M)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5820
b Fc(\021)21 b Fr(\025z)s(:M)1231 1370 y Fv(1)1266 1362
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5821
y Fu(.)k(By)g(the)f(v)l(ariable)i(con)n(v)n(en)n(tion)e(w)n(e)h(ma)n(y)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5822
f(assume)h(that)f Fr(z)h Fc(6\021)c Fr(x;)12 b(y)28 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5823
Fu(and)563 1453 y Fr(z)g Fu(is)f(not)e(free)i(in)e Fr(N)t(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5824
b(L)p Fu(.)26 b(Then)f(b)n(y)g(induction)g(h)n(yp)r(othesis)799
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5825
1577 y(\()p Fr(\025z)s(:M)1008 1585 y Fv(1)1043 1577
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5826
y Fu(\)[)p Fr(x)c Fu(:=)g Fr(N)8 b Fu(][)p Fr(y)25 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5827
Fu(:=)d Fr(L)p Fu(])47 b Fc(\021)g Fr(\025z)s(:)p Fu(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5828
Fr(M)1974 1585 y Fv(1)2009 1577 y Fu([)p Fr(x)21 b Fu(:=)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5829
Fr(N)8 b Fu(][)p Fr(y)25 b Fu(:=)c Fr(L)p Fu(]\))1658
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5830
1678 y Fc(\021)47 b Fr(\025z)s(:)p Fu(\()p Fr(M)1974
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5831
1686 y Fv(1)2009 1678 y Fu([)p Fr(y)24 b Fu(:=)e Fr(L)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5832
Fu(][)p Fr(x)f Fu(:=)h Fr(N)8 b Fu([)p Fr(y)25 b Fu(:=)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5833
Fr(L)p Fu(]]\))1658 1778 y Fc(\021)47 b Fu(\()p Fr(\025z)s(:M)1974
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5834
1786 y Fv(1)2009 1778 y Fu(\)[)p Fr(y)24 b Fu(:=)e Fr(L)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5835
Fu(][)p Fr(x)f Fu(:=)h Fr(N)8 b Fu([)p Fr(y)24 b Fu(:=)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5836
Fr(L)p Fu(]].)563 1902 y Fs(Case)31 b(3:)d Fr(M)33 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5837
Fc(\021)25 b Fr(M)1140 1910 y Fv(1)1175 1902 y Fr(M)1249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5838
1910 y Fv(2)1284 1902 y Fu(.)j(The)g(statemen)n(t)f(follo)n(ws)k(again)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5839
e(from)f(the)f(induction)h(h)n(yp)r(othesis.)3291 1994
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5840
y Fb(\003)p 3435 2049 V 523 2052 2915 4 v 523 2199 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5841
Fs(Fig.)15 b(2.)29 b Fu(The)g(informal)h(pro)r(of)h(of)f(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5842
(substitution)g(lemma)g(copied)g(from)g([3].)i(In)e(the)g(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5843
(da-)523 2291 y(case,)35 b(the)f(v)l(ariable)g(con)n(v)n(en)n(tion)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5844
(allo)n(ws)j(Barendregt)f(to)f(mo)n(v)n(e)f(the)g(substitutions)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5845
(under)f(the)523 2382 y(binder,)25 b(to)h(apply)g(the)f(induction)g(h)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5846
(yp)r(othesis)h(and)f(then)g(to)h(pull)f(out)h(the)f(substitutions.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5847
Black 523 2718 a Fx(and)d Fm(L)p Fx(\).)f(If)h(w)n(e)g(w)n(ould)f(pro)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5848
(v)n(e)f(the)i(substitution)g(lemma)g(b)n(y)g(induction)g(o)n(v)n(er)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5849
(the)i(de\014nition)523 2817 y(of)30 b Fm(\003)678 2829
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5850
y Fj(\013)725 2817 y Fx(,)g(then)h(w)n(e)e(w)n(ould)h(need)g(to)g(sho)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5851
(w)f(the)i(lam)n(b)r(da-case)d(for)h Fo(al)t(l)40 b Fm(z)t
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5852
Fx(,)30 b(not)g(just)g(the)h(ones)523 2917 y(b)r(eing)f(suitably)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5853
(fresh.)h(This)f(w)n(ould)g(mean)h(w)n(e)f(ha)n(v)n(e)f(to)i(rename)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5854
(binders)g(and)g(establish)523 3016 y(a)d(n)n(um)n(b)r(er)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5855
(auxiliary)f(lemmas)h(concerning)f(suc)n(h)i(renamings.)e(In)h(this)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5856
(section)f(w)n(e)g(will)523 3116 y(deriv)n(e)33 b(an)g(induction)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5857
(principle)g(whic)n(h)f(allo)n(ws)g(a)g(similar)g(con)n(v)n(enien)n(t)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5858
(reasoning)g(as)h(in)523 3216 y(Barendregt's)26 b(informal)h(pro)r(of.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5859
648 3340 y(F)-7 b(or)39 b(this)h(w)n(e)f(only)h(consider)e(induction)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5860
(h)n(yp)r(otheses)f(of)h(the)g(form)g Fm(P)55 b(t)43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5861
b(x)p Fx(,)e(where)523 3439 y Fm(P)49 b Fx(is)36 b(the)h(prop)r(ert)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5862
(y)e(to)i(b)r(e)g(pro)n(v)n(ed;)e Fm(P)48 b Fx(dep)r(ends)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5863
b(on)f(a)h(v)-5 b(ariable)35 b Fm(t)j Fl(2)g Fm(\003)2925
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5864
3451 y Fj(\013)3009 3439 y Fx(\(o)n(v)n(er)d(whic)n(h)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5865
3539 y(the)i(induction)h(is)f(done\),)g(and)g(a)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5866
b(ariable)36 b Fm(x)h Fx(standing)g(for)f(the)i(\\other")d(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5867
b(ariables)36 b(or)523 3639 y Fo(c)l(ontext)31 b Fx(of)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5868
b(the)h(induction.)g(Since)f Fm(x)h Fx(is)g(allo)n(w)n(ed)d(to)j(b)r(e)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5869
f(a)g(tuple,)h(sev)n(eral)e(v)-5 b(ariables)23 b(can)h(b)r(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5870
3738 y(enco)r(ded.)g(In)g(case)f(of)h(the)h(substitution)f(lemma)g(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5871
(Fig.)g(2)g(the)g(notation)f Fm(P)35 b(t)23 b(x)i Fx(should)f(b)r(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5872
3838 y(understo)r(o)r(d)31 b(as)g(follo)n(ws:)f(the)i(induction)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5873
b(ariable)30 b Fm(t)i Fx(is)f Fm(M)9 b Fx(,)32 b(the)f(con)n(text)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5874
Fm(x)h Fx(is)g(the)g(tuple)523 3938 y(\()p Fm(x;)14 b(y)s(;)g(N)t(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5875
(L)p Fx(\))28 b(and)f(the)h(induction)g(h)n(yp)r(othesis)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5876
Fm(P)40 b Fx(is)755 4169 y Fm(\025M)t(:)47 b(\025)p Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5877
Fm(x;)14 b(y)s(;)g(N)t(;)g(L)p Fx(\))p Fm(:)47 b(M)9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5878
b Fx([)p Fm(x)23 b Fx(:=)f Fm(N)9 b Fx(][)p Fm(y)26 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5879
Fx(:=)d Fm(L)p Fx(])f Fl(\021)h Fm(M)9 b Fx([)p Fm(y)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5880
b Fx(:=)e Fm(L)p Fx(][)p Fm(x)g Fx(:=)g Fm(N)9 b Fx([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5881
Fm(y)25 b Fx(:=)e Fm(L)p Fx(]])523 4425 y(where)h(w)n(e)h(use)f(Isab)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5882
(elle's)g(con)n(v)n(enien)n(t)g(tuple-notation)g(for)g(the)h(second)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5883
(lam)n(b)r(da-abstrac-)523 4525 y(tion)30 b([11].)f(So)h(b)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5884
(writing)g Fm(P)39 b(t)27 b(x)j Fx(w)n(e)g(just)g(mak)n(e)f(explicit)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5885
(all)g(the)g(v)-5 b(ariables)28 b(in)n(v)n(olv)n(ed)h(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5886
4625 y(the)f(induction.)648 4749 y(F)-7 b(rom)23 b(the)i(inductiv)n(e)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5887
(de\014nition)g(of)g Fm(\003)1872 4761 y Fj(\013)1943
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5888
4749 y Fx(w)n(e)g(can)f(deriv)n(e)g(a)h(structural)f(induction)h(prin-)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5889
523 4848 y(ciple)36 b(that)g(requires)f(to)h(pro)n(v)n(e)e(the)j(lam)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5890
(b)r(da-case)d(for)i(binders)f(that)h(are)f(fresh)h(for)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5891
4948 y(con)n(text)27 b Fm(x)p Fx(|this)i(is)e(what)h(the)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5892
b(ariable)26 b(con)n(v)n(en)n(tion)g(assumes.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5893
Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5894
%%Page: 11 11
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5895
TeXDict begin 11 10 bop Black Black Black 523 448 a Ff(Lemma)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5896
b(10)p Black 41 w(\(Induction)f(Principle\).)g Fx(Giv)n(en)c(an)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5897
(induction)f(h)n(yp)r(othesis)h Fm(P)34 b(t)23 b(x)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5898
Fx(with)523 548 y Fm(t)c Fl(2)g Fm(\003)712 560 y Fj(\013)787
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5899
548 y Fx(and)28 b Fm(x)23 b Fl(2)g Fo(fs-pset)q Fx(,)k(then)i(pro)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5900
(ving)d(the)i(follo)n(wing:)p Black 581 751 a Fl(\017)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5901
Black 41 w(8)p Fm(x)23 b(a:)g(P)35 b Fe(am)o Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5902
Fm(a)p Fx(\))23 b Fm(x)p Black 581 859 a Fl(\017)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5903
41 w(8)p Fm(x)g(t)811 871 y Fw(1)871 859 y Fm(t)901 871
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5904
y Fw(2)938 859 y Fm(:)g(P)35 b(t)1102 871 y Fw(1)1163
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5905
859 y Fm(x)19 b Fl(^)f Fm(P)35 b(t)1420 871 y Fw(2)1480
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5906
859 y Fm(x)47 b Fl(\))23 b Fm(P)35 b Fe(pr)o Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5907
Fm(t)1917 871 y Fw(1)1955 859 y Fm(;)14 b(t)2022 871
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5908
y Fw(2)2059 859 y Fx(\))23 b Fm(x)p Black 581 968 a Fl(\017)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5909
Black 41 w(8)p Fm(x)g(a:)g(a)g Fx(#)g Fm(x)47 b Fl(\))f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5910
Fx(\()p Fl(8)p Fm(t:)22 b(P)35 b(t)23 b(x)47 b Fl(\))f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5911
Fm(P)35 b Fx([)p Fm(a)p Fx(])p Fm(:t)23 b(x)p Fx(\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5912
1162 y(giv)n(es)j Fl(8)p Fm(t)d(x:)g(P)35 b(t)23 b(x)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5913
Fx(.)p Black 523 1373 a Fo(Pr)l(o)l(of.)p Black 43 w
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5914
Fx(By)38 b(induction)h(o)n(v)n(er)d(the)i(de\014nition)h(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5915
Fm(\003)2188 1385 y Fj(\013)2235 1373 y Fx(.)g(W)-7 b(e)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5916
b(need)f(to)g(strengthen)g(the)g(in-)523 1472 y(duction)h(h)n(yp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5917
(othesis)g(to)g Fl(8)p Fm(t)i(\031)k(x:)e(P)53 b Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5918
Fm(\031)1879 1481 y Fi(\001)1918 1472 y Fm(t)p Fx(\))43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5919
b Fm(x)p Fx(,)c(that)g(means)g(considering)e Fm(t)j Fx(under)e(all)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5920
1572 y(p)r(erm)n(utations)30 b Fm(\031)s Fx(.)h(Only)f(the)h(case)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5921
(for)h(terms)g(of)h(the)f(form)g([)p Fm(a)p Fx(])p Fm(:t)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5922
Fx(will)g(b)r(e)g(explained.)f(W)-7 b(e)523 1672 y(need)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5923
b(to)h(sho)n(w)e(that)h Fm(P)36 b Fx(\()p Fm(\031)1377
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5924
1681 y Fi(\001)1416 1672 y Fx([)p Fm(a)p Fx(])p Fm(:t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5925
Fx(\))25 b Fm(x)p Fx(,)k(where)e Fm(\031)2005 1681 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5926
Fi(\001)2044 1672 y Fx([)p Fm(a)p Fx(])p Fm(:t)d Fx(=)g([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5927
Fm(\031)2373 1681 y Fi(\001)2411 1672 y Fm(a)p Fx(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5928
Fm(:)p Fx(\()p Fm(\031)2583 1681 y Fi(\001)2622 1672
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5929
y Fm(t)p Fx(\))29 b(b)n(y)f(Def.)h(5\()p Fm(i)p Fx(\).)f(By)g(IH,)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5930
1771 y(\()p Fl(\003)597 1741 y Fw(1)634 1771 y Fx(\))33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5931
b Fl(8)p Fm(\031)h(x:)e(P)43 b Fx(\()p Fm(\031)1107 1780
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5932
y Fi(\001)1146 1771 y Fm(t)p Fx(\))31 b Fm(x)j Fx(holds.)e(Since)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5933
Fm(x;)14 b(\031)1921 1780 y Fi(\001)1960 1771 y Fm(t;)g(\031)2077
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5934
1780 y Fi(\001)2115 1771 y Fm(a)31 b Fl(2)h Fo(fs-pset)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5935
Fx(holds,)f(one)g(can)h(deriv)n(e)e(b)n(y)523 1871 y(Lem.)j(5)g(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5936
(there)f(is)h(a)g Fm(c)g Fx(suc)n(h)f(that)h(\()p Fl(\003)1907
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5937
1841 y Fw(2)1944 1871 y Fx(\))h Fm(c)e Fx(#)h(\()p Fm(x;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5938
b(\031)2349 1880 y Fi(\001)2388 1871 y Fm(t;)g(\031)2505
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5939
1880 y Fi(\001)2544 1871 y Fm(a)p Fx(\).)34 b(F)-7 b(rom)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5940
b Fm(c)h Fx(#)g Fm(x)g Fx(and)g(the)523 1970 y(assumption,)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5941
b(one)f(can)h(further)f(deriv)n(e)g(\()p Fl(8)p Fm(t:)d(P)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5942
b(t)26 b(x)51 b Fl(\))f Fm(P)37 b Fx([)p Fm(c)p Fx(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5943
Fm(:t)26 b(x)p Fx(\).)k(Giv)n(en)e(\()p Fl(\003)3052
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5944
1940 y Fw(1)3089 1970 y Fx(\))i(w)n(e)e(ha)n(v)n(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5945
2070 y(that)j Fm(P)39 b Fx(\(\()p Fm(c)j(\031)990 2079
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5946
y Fi(\001)1028 2070 y Fm(a)p Fx(\))14 b(::)g Fm(\031)1242
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5947
2079 y Fi(\001)1294 2070 y Fm(t)p Fx(\))28 b Fm(x)i Fx(holds)g(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5948
(th)n(us)g(also)g Fm(P)39 b Fx(\([)p Fm(c)p Fx(])p Fm(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5949
Fx(\(\()p Fm(c)j(\031)2621 2079 y Fi(\001)2660 2070 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5950
Fm(a)p Fx(\))14 b(::)g Fm(\031)2873 2079 y Fi(\001)2925
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5951
2070 y Fm(t)p Fx(\)\))28 b Fm(x)p Fx(.)j(Because)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5952
2170 y(of)d(\()p Fl(\003)692 2140 y Fw(2)729 2170 y Fx(\))h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5953
Fm(c)24 b Fl(6)p Fx(=)f Fm(\031)988 2179 y Fi(\001)1027
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5954
2170 y Fm(a)28 b Fx(and)g Fm(c)c Fx(#)g Fm(\031)1464
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5955
2179 y Fi(\001)1502 2170 y Fm(t)p Fx(,)29 b(and)f(b)n(y)f(Def.)i(5\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5956
Fm(ii)p Fx(\))f(w)n(e)g(ha)n(v)n(e)f(that)h([)p Fm(c)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5957
Fx(])p Fm(:)p Fx(\(\()p Fm(c)42 b(\031)3022 2179 y Fi(\001)3061
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5958
2170 y Fm(a)p Fx(\))10 b(::)g Fm(\031)3267 2179 y Fi(\001)3319
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5959
2170 y Fm(t)24 b Fx(=)523 2269 y([)p Fm(\031)596 2278
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5960
y Fi(\001)635 2269 y Fm(a)p Fx(])p Fm(:)p Fx(\()p Fm(\031)807
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5961
2278 y Fi(\001)845 2269 y Fm(t)p Fx(\).)k(Therefore)f(w)n(e)g(can)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5962
(conclude)g(with)i Fm(P)34 b Fx(\()p Fm(\031)2309 2278
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5963
y Fi(\001)2348 2269 y Fx([)p Fm(a)p Fx(])p Fm(:t)p Fx(\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5964
b Fm(x)p Fx(.)766 b Fl(u)-55 b(t)648 2480 y Fx(With)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5965
b(this)f(w)n(e)g(ha)n(v)n(e)f(ac)n(hiev)n(ed)g(what)i(w)n(e)f(set)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5966
(out)g(in)h(the)f(in)n(tro)r(duction:)g(w)n(e)g(ha)n(v)n(e)f(a)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5967
2580 y(represen)n(tation)17 b(for)h Fm(\013)p Fx(-equiv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5968
b(alen)n(t)19 b(lam)n(b)r(da-terms)e(based)h(on)g(names)h(\(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5969
(example)g([)p Fm(\025a:t)p Fx(])3390 2592 y Fj(\013)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5970
2680 y Fx(is)23 b(represen)n(ted)f(b)n(y)g([)p Fm(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5971
Fx(])p Fm(:t)p Fx(\))i(and)f(w)n(e)f(ha)n(v)n(e)g(an)h(induction)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5972
(principle)g(where)f(the)i(lam)n(b)r(da-case)523 2779
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5973
y(needs)31 b(to)g(b)r(e)h(pro)n(v)n(ed)d(for)i(binders)g(that)g(are)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5974
(fresh)h(w.r.t.)g(the)h(v)-5 b(ariables)30 b(in)h(the)g(con)n(text)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5975
2879 y(of)26 b(the)g(induction,)g(i.e.,)g(w)n(e)g(can)f(reason)g(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5976
(if)h(w)n(e)g(had)f(emplo)n(y)n(ed)g(a)h(v)-5 b(ariable)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5977
b(con)n(v)n(en)n(tion.)523 3190 y Fp(5)112 b(Examples)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5978
3435 y Fx(It)35 b(is)f(reasonably)f(straigh)n(tforw)n(ard)f(to)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5979
(implemen)n(t)h(the)g(results)f(from)g(Sec.)h(3)f(and)h(4)f(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5980
3535 y(Isab)r(elle/HOL:)25 b(the)h(set)h Fm(\010)f Fx(is)g(an)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5981
(inductiv)n(e)g(datat)n(yp)r(e,)g(the)g(pset)g(and)g(fs-pset)g(prop)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5982
(erties)523 3635 y(can)20 b(b)r(e)g(form)n(ulated)f(as)h(axiomatic)f(t)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5983
n(yp)r(e-classes)f([20],)h(and)h(the)h(subset)f Fm(\003)2863
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5984
3647 y Fj(\013)2930 3635 y Fx(can)f(b)r(e)i(de\014ned)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5985
3734 y(using)31 b(the)h(Isab)r(elle's)f Fe(typedef)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5986
Fx(-mec)n(hanism.)f(This)i(section)f(fo)r(cuses)h(on)f(ho)n(w)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5987
(reasoning)523 3834 y(o)n(v)n(er)26 b Fm(\003)759 3846
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5988
y Fj(\013)833 3834 y Fx(pans)i(out)f(in)h(practice.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5989
3943 y(The)38 b(\014rst)h(obstacle)f(is)h(that)g(so)f(far)g(Isab)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5990
(elle's)g(datat)n(yp)r(e)h(pac)n(k)-5 b(age)37 b(is)i(not)f(general)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5991
4042 y(enough)33 b(to)h(allo)n(w)f(a)h(direct)g(de\014nition)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5992
(functions)g(o)n(v)n(er)f Fm(\003)2545 4054 y Fj(\013)2592
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5993
4042 y Fx(:)h(although)f Fm(\003)3059 4054 y Fj(\013)3140
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5994
4042 y Fx(con)n(tains)523 4142 y(only)i(terms)h(of)f(the)h(form)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5995
Fe(am)o Fx(\()p Fm(a)p Fx(\),)g Fe(pr)o Fx(\()p Fm(t)1814
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5996
4154 y Fw(1)1852 4142 y Fm(;)14 b(t)1919 4154 y Fw(2)1956
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5997
4142 y Fx(\))36 b(and)f([)p Fm(a)p Fx(])p Fm(:t)p Fx(,)h(pattern-matc)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5998
(hing)f(in)g(Isab)r(elle)523 4241 y(requires)h(the)j(injectivit)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5999
(of)g(term-constructors.)d(But)j(clearly)-7 b(,)37 b([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6000
Fm(a)p Fx(])p Fm(:t)h Fx(is)f Fo(not)46 b Fx(injectiv)n(e.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6001
4341 y(F)-7 b(ortunately)g(,)37 b(one)f(can)h(w)n(ork)e(around)h(this)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6002
(obstacle)f(b)n(y)-7 b(,)37 b(roughly)f(sp)r(eaking,)g(de\014ning)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6003
4441 y(functions)h(as)g(inductiv)n(e)g(relations)e(and)i(then)h(use)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6004
(the)g(de\014nite)g(description)g(op)r(erator)523 4540
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6005
y Fo(THE)h Fx(of)28 b(Isab)r(elle)f(to)g(turn)h(the)g(relations)f(in)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6006
(to)g(functions.)648 4649 y(W)-7 b(e)30 b(giv)n(e)f(an)h(example:)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6007
(capture-a)n(v)n(oiding)e(substitution)k(can)e(b)r(e)i(de\014ned)f(as)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6008
(a)h(four-)523 4749 y(place)21 b(relation)g(\(the)i(\014rst)e(argumen)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6009
(t)g(con)n(tains)g(the)h(term)g(in)n(to)f(whic)n(h)h(something)f(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6010
(b)r(eing)523 4848 y(substituted,)35 b(the)g(second)e(the)i(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6011
b(ariable)33 b(that)i(is)f(substituted)h(for,)f(the)g(third)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6012
(term)523 4948 y(that)28 b(is)f(substituted,)i(and)e(the)h(last)g(con)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6013
(tains)e(the)i(result)g(of)f(the)h(substitution\):)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6014
Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6015
%%Page: 12 12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6016
TeXDict begin 12 11 bop Black Black Black Black 535 526
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6017
a Fe(consts)41 b(Subst)g(::)i("\()p Fm(\003)1378 538
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6018
y Fj(\013)1443 526 y Fl(\002)18 b Fk(A)41 b Fl(\002)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6019
b Fm(\003)1745 538 y Fj(\013)1810 526 y Fl(\002)h Fm(\003)1952
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6020
538 y Fj(\013)1998 526 y Fe(\))44 b(set")535 626 y(inductive)c(Subst)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6021
535 726 y(intros)535 825 y(s1:)27 b("\(am)o(\(a\),a,t',t'\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6022
Fl(2)p Fe(Subst)o(")535 925 y(s2:)g("a)p Fl(6)p Fx(=)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6023
Fe(b)42 b Fx(=)-14 b Fl(\))44 b Fe(\(am)n(\(b\),a,t',am)l(\(b\)\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6024
Fl(2)p Fe(Subst")535 1024 y(s3:)27 b(")p Fa(J)p Fe(\(s)859
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6025
1036 y Fw(1)896 1024 y Fe(,a,t',s)1204 1036 y Fw(1)1224
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6026
1024 y Fe('\))p Fl(2)p Fe(Subst;)41 b(\(s)1760 1036 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6027
Fw(2)1796 1024 y Fe(,a,t',s)2104 1036 y Fw(2)2125 1024
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6028
y Fe('\))p Fl(2)p Fe(Subst)p Fa(K)1834 1124 y Fx(=)-14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6029
b Fl(\))43 b Fe(\(pr)o(\(s)2230 1136 y Fw(1)2266 1124
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6030
y Fe(,s)2354 1136 y Fw(2)2391 1124 y Fe(\),a,t',pr)l(\(s)2871
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6031
1136 y Fw(1)2894 1124 y Fe(',s)3026 1136 y Fw(2)3048
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6032
1124 y Fe('\)\))p Fl(2)p Fe(Subst")535 1224 y(s4:)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6033
b(")p Fa(J)p Fe(b)p Fx(#)p Fe(\(a,t'\);\(s,a,t',s')o(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6034
Fl(2)p Fe(Su)o(bst)o Fa(K)38 b Fx(=)-14 b Fl(\))43 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6035
Fe(\([b].s,a,t',[b].s)o('\))p Fl(2)p Fe(Su)o(bs)o(t")523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6036
1375 y Fx(While)32 b(on)g(\014rst)f(sigh)n(t)g(this)h(relation)f(lo)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6037
(oks)g(as)g(if)h(it)g(de\014ned)g(a)f(non-total)g(function,)h(one)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6038
1475 y(should)22 b(b)r(e)g(careful!)f(Clearly)-7 b(,)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6039
b(the)h(lam)n(b)r(da-case)e(\(i.e.)44 b Fe(\([b].s,a,t',[b].s)o('\))16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6040
b Fl(2)24 b Fe(Subst)n Fx(\))523 1575 y(holds)34 b(only)f(under)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6041
(precondition)f Fe(b)p Fx(#)p Fe(\(a,s\))p Fx(|roughly)e(meaning)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6042
(that)h Fm(a)g Fl(6)p Fx(=)f Fm(b)g Fx(and)523 1674 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6043
Fm(b)c Fx(cannot)f(o)r(ccur)g(freely)h(in)g Fm(s)p Fx(.)g(Ho)n(w)n(ev)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6044
(er,)e Fe(Subst)g Fo(do)l(es)37 b Fx(de\014ne)29 b(a)f(total)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6045
(function,)g(b)r(ecause)523 1774 y Fe(Subst)i Fx(is)h(de\014ned)h(o)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6046
(v)n(er)e Fm(\013)p Fx(-equiv)-5 b(alen)n(t)32 b(lam)n(b)r(da-terms)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6047
(\(more)g(precisely)g Fm(\003)2996 1786 y Fj(\013)3043
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6048
1774 y Fx(\),)h Fo(not)40 b Fx(o)n(v)n(er)523 1873 y(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6049
(da-terms.)27 b(W)-7 b(e)28 b(can)f(indeed)h(sho)n(w)e(\\totalit)n(y":)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6050
p Black 523 2020 a Ff(Lemma)k(11.)p Black 40 w Fo(F)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6051
b(or)30 b(al)t(l)h Fe(t)1343 2032 y Fw(1)1380 2020 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6052
Fo(,)f Fe(a)p Fo(,)g Fe(t)1578 2032 y Fw(2)1614 2020
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6053
y Fo(,)h Fl(9)p Fe(t)1760 2032 y Fw(3)1797 2020 y Fm(:)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6054
b Fx(\()p Fe(t)1919 2045 y Fw(1)1956 2020 y Fm(;)14 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6055
Fe(a)p Fm(;)g Fe(t)2117 2041 y Fw(2)2154 2020 y Fm(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6056
Fe(t)2235 2041 y Fw(3)2272 2020 y Fx(\))23 b Fl(2)h Fe(Subst)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6057
Fm(:)p Black 523 2167 a Fo(Pr)l(o)l(of.)p Black 43 w
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6058
Fx(The)f(pro)r(of)f(in)h(Isab)r(elle/HOL)e(uses)h(the)h(induction)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6059
(principle)f(deriv)n(ed)g(in)h(Thm.)g(10.)523 2267 y(It)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6060
b(is)f(as)g(follo)n(ws:)p Black Black 546 2384 a Fe(proof)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6061
b(\(nominal)p 1165 2384 27 4 v 28 w(induct)65 b(t)1561
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6062
2396 y Fw(1)1598 2384 y Fe(\))664 2484 y(case)42 b(\(1)h(b\))g(\(*)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6063
(variable)f(case)h(*\))664 2583 y(show)g(")p Fl(9)p Fe(t)1016
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6064
2595 y Fw(3)1053 2583 y Fe(.)h(\(am\(b\),a,t)1580 2595
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6065
y Fw(2)1613 2583 y Fe(,t)1701 2595 y Fw(3)1737 2583 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6066
Fe(\))p Fl(2)p Fe(Subst")e(by)i(\(cases)e("b=a"\))g(\(force+\))546
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6067
2683 y(next)664 2783 y(case)h(\(2)h(s)1057 2795 y Fw(1)1137
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6068
2783 y Fe(s)1181 2795 y Fw(2)1218 2783 y Fe(\))g(\(*)g(application)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6069
(case)j(*\))664 2882 y(thus)g(")p Fl(9)p Fe(t)1016 2894
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6070
y Fw(3)1053 2882 y Fe(.)h(\(pr\(s)1360 2894 y Fw(1)1395
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6071
2882 y Fe(,s)1483 2894 y Fw(2)1519 2882 y Fe(\),a,t)1739
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6072
2894 y Fw(2)1775 2882 y Fe(,t)1863 2894 y Fw(3)1899 2882
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6073
y Fe(\))p Fl(2)p Fe(Subst")e(by)i(force)546 2982 y(next)664
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6074
3081 y(case)f(\(3)h(b)g(s\))g(\(*)g(lambda)e(case)h(*\))664
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6075
3181 y(thus)g(")p Fl(9)p Fe(t)1016 3193 y Fw(3)1053 3181
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6076
y Fe(.)h(\([b].s,a,t)1580 3193 y Fw(2)1613 3181 y Fe(,t)1701
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6077
3193 y Fw(3)1737 3181 y Fe(\))p Fl(2)p Fe(Subst")e(by)i(force)546
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6078
3281 y(qed)523 3421 y Fx(The)21 b(induction)g(metho)r(d)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6079
Fe(nominal)p 1657 3421 V 29 w(induct)d Fx(brings)i(the)h(induction)g(h)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6080
n(yp)r(othesis)f(automat-)523 3521 y(ically)27 b(in)n(to)g(the)h(form)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6081
1031 3676 y(\()p Fm(\025)p Fe(t)1155 3688 y Fw(1)1207
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6082
3676 y Fm(\025)p Fx(\()p Fe(a)p Fm(;)14 b Fe(t)1412 3688
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6083
y Fw(2)1449 3676 y Fx(\))p Fm(:)g Fl(9)p Fe(t)1608 3688
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6084
y Fw(3)1645 3676 y Fm(:)p Fx(\()p Fe(t)1744 3688 y Fw(1)1781
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6085
3676 y Fm(;)g Fe(a)p Fm(;)g Fe(t)1943 3688 y Fw(2)1979
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6086
3676 y Fm(;)g Fe(t)2060 3688 y Fw(3)2097 3676 y Fx(\))23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6087
b Fl(2)h Fe(Subst)m Fx(\))1031 3732 y Fh(|)p 1068 3732
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6088
651 10 v 651 w({z)p 1793 3732 V 651 w(})1730 3810 y Fj(P)2552
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6089
3676 y Fe(t)2596 3688 y Fw(1)2518 3723 y Fh(|{z})2580
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6090
3798 y Fj(t)2704 3676 y Fx(\()p Fe(a)p Fm(;)14 b Fe(t)2861
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6091
3688 y Fw(2)2898 3676 y Fx(\))2704 3732 y Fh(|)p 2741
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6092
3732 39 10 v 39 w({z)p 2854 3732 V 39 w(})2798 3806 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6093
Fj(x)523 3940 y Fx(b)n(y)37 b(collecting)g(all)h(free)f(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6094
b(ariables)37 b(in)h(the)g(goal,)e(and)i(then)g(it)g(applies)f(Thm.)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6095
(10.)f(This)523 4040 y(results)29 b(in)h(three)f(cases)g(to)g(b)r(e)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6096
(pro)n(v)n(ed|v)-5 b(ariable)27 b(case,)i(application)g(case)f(and)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6097
(lam)n(b)r(da-)523 4139 y(case.)c(The)h(requiremen)n(t)f(that)i(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6098
(con)n(text)g(\()p Fe(a)p Fm(;)14 b Fe(t)2126 4151 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6099
Fw(2)2162 4139 y Fx(\))28 b(is)e(a)h Fo(fs-pset)p Fx(-elemen)n(t)g(is)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6100
(enforced)f(b)n(y)523 4239 y(using)k(axiomatic)f(t)n(yp)r(e-classes)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6101
(and)i(relying)f(on)h(Isab)r(elle's)f(t)n(yp)r(e-system.)h(Note)g(that)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6102
g(in)523 4339 y(the)f(lam)n(b)r(da-case)f(it)h(is)g(imp)r(ortan)n(t)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6103
(to)g(kno)n(w)f(that)h(the)h(binder)f Fe(b)f Fx(is)h(fresh)g(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6104
Fe(a)f Fx(and)h Fe(t)3378 4351 y Fw(2)3415 4339 y Fx(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6105
4438 y(The)f(pro)r(of)f(obligation)f(in)i(this)g(case)f(is:)938
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6106
4593 y Fe(b)c Fx(#)g(\()p Fe(a)p Fm(;)14 b Fe(t)1254
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6107
4614 y Fw(2)1291 4593 y Fx(\))19 b Fl(^)f(9)p Fe(t)1505
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6108
4605 y Fw(3)1542 4593 y Fm(:)p Fx(\()p Fe(s)p Fm(;)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6109
Fe(a)p Fm(;)g Fe(t)1802 4614 y Fw(2)1839 4593 y Fm(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6110
Fe(t)1920 4605 y Fw(3)1957 4593 y Fx(\))47 b(implies)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6111
Fl(9)p Fe(t)2426 4605 y Fw(3)2463 4593 y Fm(:)p Fx(\([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6112
Fe(b)p Fx(])p Fm(:)p Fe(s)p Fm(;)14 b Fe(a)p Fm(;)g Fe(t)2835
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6113
4618 y Fw(2)2873 4593 y Fm(;)g Fe(t)2954 4605 y Fw(3)2990
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6114
4593 y Fx(\))523 4749 y(whic)n(h)29 b(can)f(b)r(e)i(easily)e(b)r(e)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6115
(sho)n(wn)g(b)n(y)f(rule)h Fe(s4)p Fx(.)f(As)h(a)g(result,)f(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6116
(only)e(case)g(in)i(whic)n(h)e(w)n(e)523 4848 y(really)f(need)i(to)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6117
(man)n(ually)g(\\in)n(terfere")f(is)h(in)h(the)g(v)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6118
b(ariable)27 b(case)g(where)h(w)n(e)g(ha)n(v)n(e)g(to)g(giv)n(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6119
4948 y(Isab)r(elle)f(the)h(hin)n(t)g(to)g(distinguish)f(the)h(cases)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6120
Fm(b)c Fx(=)f Fm(a)28 b Fx(and)f Fm(b)c Fl(6)p Fx(=)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6121
Fm(a)p Fx(.)778 b Fl(u)-55 b(t)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6122
%%Page: 13 13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6123
TeXDict begin 13 12 bop Black Black 523 448 a Fx(T)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6124
b(ogether)27 b(with)h(a)f(uniqueness-lemma)g(\(whose)g(pro)r(of)g(w)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6125
(e)g(omit\))h(asserting)e(that)837 621 y Fl(8)p Fe(s)928
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6126
633 y Fw(1)964 621 y Fe(s)1008 633 y Fw(2)1045 621 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6127
Fm(:)p Fx(\()p Fe(t)1144 633 y Fw(1)1181 621 y Fm(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6128
b Fe(a)p Fm(;)g Fe(t)1343 633 y Fw(2)1380 621 y Fm(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6129
Fe(s)1461 633 y Fw(1)1497 621 y Fx(\))24 b Fl(2)f Fe(Subst)17
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6130
b Fl(^)h Fx(\()p Fe(t)2017 633 y Fw(1)2054 621 y Fm(;)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6131
Fe(a)p Fm(;)g Fe(t)2216 633 y Fw(2)2253 621 y Fm(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6132
Fe(s)2334 633 y Fw(2)2370 621 y Fx(\))24 b Fl(2)f Fe(Subst)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6133
Fl(\))i Fe(s)2895 633 y Fw(1)2955 621 y Fx(=)g Fe(s)3087
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6134
633 y Fw(2)3332 621 y Fx(\(3\))523 795 y(one)k(can)g(pro)n(v)n(e)f(the)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6135
i(stronger)e(totalit)n(y-prop)r(ert)n(y)-7 b(,)26 b(namely)h(for)g(all)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6136
h Fe(t)2744 807 y Fw(1)2780 795 y Fx(,)g Fe(a)p Fx(,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6137
Fe(t)2969 807 y Fw(2)3006 795 y Fx(:)1469 968 y Fl(9)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6138
Fx(!)p Fe(t)1582 980 y Fw(3)1619 968 y Fm(:)c Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6139
Fe(t)1741 993 y Fw(1)1778 968 y Fm(;)14 b Fe(a)p Fm(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6140
Fe(t)1939 988 y Fw(2)1976 968 y Fm(;)g Fe(t)2057 988
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6141
y Fw(3)2094 968 y Fx(\))24 b Fl(2)f Fe(Subst)e Fm(:)840
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6142
b Fx(\(4\))523 1141 y(Ha)n(ving)34 b(this)h(at)g(our)f(disp)r(osal,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6143
(w)n(e)g(can)g(use)h(Isab)r(elle's)f(de\014nite)i(description)e(op)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6144
(erator)523 1241 y Fm(T)12 b(H)7 b(E)30 b Fx(and)c(turn)g(capture-a)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6145
(v)n(oiding)d(substitution)k(in)n(to)f(a)f(function;)i(w)n(e)f(write)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6146
(this)i(func-)523 1340 y(tion)h(as)f(\()p Fl(\000)p Fx(\)[\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6147
Fl(\000)p Fx(\))c(:=)g(\()p Fl(\000)p Fx(\)],)28 b(and)f(establish)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6148
(the)h(equations:)951 1591 y Fe(am)p Fx(\()p Fe(a)p Fx(\)[)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6149
Fe(a)22 b Fx(:=)h Fe(t)p Fx(])g(=)g Fe(t)951 1691 y(am)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6150
Fx(\()p Fe(b)p Fx(\)[)p Fe(a)f Fx(:=)h Fe(t)p Fx(])g(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6151
Fe(am)o Fx(\()p Fe(b)p Fx(\))760 b(pro)n(vided)22 b Fe(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6152
Fl(6)p Fx(=)f Fe(b)796 1791 y(pr)p Fx(\()p Fe(s)960 1803
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6153
y Fw(1)997 1791 y Fm(;)14 b Fe(s)1078 1803 y Fw(2)1114
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6154
1791 y Fx(\)[)p Fe(a)23 b Fx(:=)g Fe(t)p Fx(])g(=)g Fe(pr)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6155
Fx(\()p Fe(s)1688 1803 y Fw(1)1725 1791 y Fx([)p Fe(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6156
Fx(:=)g Fe(t)p Fx(])p Fm(;)14 b Fe(s)2074 1803 y Fw(2)2110
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6157
1791 y Fx([)p Fe(a)23 b Fx(:=)f Fe(t)p Fx(]\))926 1890
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6158
y(\([)p Fe(b)p Fx(])p Fm(:)p Fe(s)p Fx(\)[)p Fe(a)g Fx(:=)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6159
Fe(t)p Fx(])g(=)g([)p Fe(b)p Fx(])p Fm(:)p Fx(\()p Fe(s)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6160
Fx([)p Fe(a)f Fx(:=)h Fe(t)p Fx(]\))467 b(pro)n(vided)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6161
b Fe(b)h Fx(#)g(\()p Fe(a)p Fm(;)14 b Fe(t)p Fx(\))3332
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6162
1742 y(\(5\))523 2060 y(These)24 b(equations)f(can)h(b)r(e)g(supplied)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6163
(to)g(Isab)r(elle's)g(simpli\014er)g(and)f(one)h(can)g(reason)e(ab)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6164
(out)523 2159 y(substitution)30 b(\\just)g(lik)n(e)f(on)h(pap)r(er".)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6165
(F)-7 b(or)29 b(this)h(w)n(e)f(giv)n(e)g(in)h(Fig.)g(3)f(one)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6166
Fo(simple)38 b Fx(example)523 2259 y(as)25 b(evidence|giving)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6167
(whole)g(formalised)f(Ch)n(urc)n(h-Rosser)e(pro)r(of)j(from)f([3,)j(p.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6168
f(60{62])523 2359 y(w)n(ould)36 b(b)r(e)g(b)r(ey)n(ond)f(the)i(space)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6169
(constrain)n(ts)f(of)i(this)g(pap)r(er.)g(The)g(complete)g(formalisa-)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6170
523 2458 y(tions)c(of)h(all)f(the)h(results,)g(the)g(Ch)n(urc)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6171
(h-Rosser)d(and)i(strong)g(normalisation)f(pro)r(of)h(is)g(at)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6172
2558 y Fe(http://www.mathe)o(mat)o(ik)o(.un)o(i-)o(mu)o(enc)o(he)o(n.d)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6173
o(e/)-11 b Fl(\030)9 b Fe(urban/nominal/)18 b Fx(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6174
2816 y Fp(6)112 b(Related)37 b(W)-9 b(ork)523 3008 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6175
Fx(There)21 b(are)f(man)n(y)g(approac)n(hes)f(to)i(formal)f(treatmen)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6176
(ts)h(of)g(binders;)g(this)g(section)g(describ)r(es)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6177
3107 y(the)28 b(ones)f(from)g(whic)n(h)h(w)n(e)f(ha)n(v)n(e)f(dra)n(wn)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6178
h(inspiration.)648 3207 y(Our)g(w)n(ork)h(uses)g(man)n(y)g(ideas)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6179
(from)g(the)h(nominal)g(logic)e(w)n(ork)h(b)n(y)g(Pitts)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6180
Fo(et)h(al)f Fx([16,)13 b(6].)523 3306 y(The)32 b(main)g(di\013erence)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6181
(is)f(that)i(b)n(y)e(constructing,)g(so)g(to)h(sa)n(y)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6182
b(,)31 b(an)h(explicit)g(mo)r(del)g(of)g(the)523 3406
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6183
y Fm(\013)p Fx(-equated)22 b(lam)n(b)r(da-terms)f(based)g(on)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6184
(functions,)g(w)n(e)g(ha)n(v)n(e)e(no)i(problem)f(with)i(the)f(axiom-)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6185
523 3506 y(of-c)n(hoice.)29 b(This)i(is)f(imp)r(ortan)n(t.)g(F)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6186
b(or)30 b(consider)g(the)g(alternativ)n(e:)g(if)h(the)g(axiom-of-c)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6187
(hoice)523 3605 y(causes)e(inconsistencies,)f(then)i(one)f(cannot)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6188
(build)h(a)f(framew)n(ork)f(for)h(binding)g(on)h(top)f(of)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6189
3705 y(Isab)r(elle/HOL)37 b(with)h(its)g(ric)n(h)f(reasoning)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6190
(infrastructure.)h(One)g(w)n(ould)h(ha)n(v)n(e)e(to)i(in)n(ter-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6191
3805 y(face)31 b(on)h(a)f(lo)n(w)n(er)f(lev)n(el)h(and)g(has)g(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6192
(redo)g(the)h(e\013ort)f(that)h(has)f(b)r(een)h(sp)r(end)f(to)h(dev)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6193
(elop)523 3904 y(Isab)r(elle/HOL.)27 b(This)g(w)n(as)g(attempted)h(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6194
([5],)f(but)h(the)g(attempt)h(w)n(as)d(later)h(abandoned.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6195
4004 y(Closely)d(related)g(to)h(our)f(w)n(ork)f(is)i([9])g(b)n(y)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6196
(Gordon)g(and)h(Melham;)g(it)g(has)g(b)r(een)g(applied)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6197
4104 y(and)c(further)h(dev)n(elop)r(ed)f(b)n(y)g(Norrish)g([13].)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6198
(This)i(w)n(ork)e(states)h(\014v)n(e)g(axioms)g(c)n(haracterising)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6199
4203 y Fm(\013)p Fx(-equiv)-5 b(alence)19 b(and)g(then)h(sho)n(ws)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6200
(that)i(a)f(mo)r(del)g(based)g(on)g(de-Bruijn)g(indices)g(satis\014es)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6201
(the)523 4303 y(axioms.)28 b(This)g(is)h(somewhat)f(similar)g(to)g(our)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6202
g(approac)n(h)f(where)h(w)n(e)h(construct)f(explicitly)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6203
4402 y(the)22 b(set)f Fm(\003)841 4414 y Fj(\013)888
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6204
4402 y Fx(.)g(In)g([9])g(they)g(giv)n(e)f(an)h(induction)h(principle)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6205
(that)g(requires)f(in)h(the)h(lam)n(b)r(da-case)523 4502
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6206
y(to)28 b(pro)n(v)n(e)d(\(using)j(their)g(notation\))1128
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6207
4675 y Fl(8)14 b Fm(x)g(t:)22 b Fx(\()p Fl(8)14 b Fm(v)s(:)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6208
b(P)i Fx(\()p Fm(t)p Fx([)p Fm(x)f Fx(:=)f Fo(V)-8 b(AR)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6209
b Fm(v)s Fx(]\)\))f(=)-14 b Fl(\))23 b Fm(P)i Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6210
Fo(LAM)37 b Fm(x)24 b(t)p Fx(\))523 4848 y(That)30 b(means)g(they)g(ha)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6211
n(v)n(e)f(to)i(pro)n(v)n(e)d Fm(P)12 b Fx(\()p Fo(LAM)41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6212
b Fm(x)28 b(t)p Fx(\))j(for)f(a)f(v)-5 b(ariable)30 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6213
Fm(x)g Fx(for)g(whic)n(h)g(nothing)523 4948 y(can)40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6214
b(b)r(e)i(assumed;)e(explicit)h Fm(\013)p Fx(-renamings)e(are)h(then)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6215
(necessary)e(in)i(order)f(to)g(get)h(the)p Black Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6216
eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6217
%%Page: 14 14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6218
TeXDict begin 14 13 bop Black Black Black 523 789 2915
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6219
4 v 523 3451 4 2662 v 587 884 a Ft(lemma)40 b(substitution)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6220
1295 884 24 4 v 31 w(lemma:)587 985 y(assumes)h(a1:)f("x)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6221
b Fc(6)p Fu(=)f Ft(y")747 1085 y(and)40 b(a2:)g("x)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6222
b Fu(#)e Ft(L")587 1186 y(shows)40 b("M[x:=N][y:=L])j(=)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6223
(M[y:=L][x:=N[y:=L]]")587 1286 y(proof)h(\(nominal)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6224
1139 1286 V 30 w(induct)h(M\))634 1387 y(case)f(\(1)g(z\))g(\(*)f(case)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6225
h(1:)g(variables)h(*\))634 1487 y(have)f("z)p Fu(=)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6226
Ft(x)g Fc(_)f Ft(\(z)p Fc(6)p Fu(=)p Ft(x)h Fc(^)f Ft(z)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6227
Fu(=)p Ft(y\))h Fc(_)f Ft(\(z)p Fc(6)p Fu(=)p Ft(x)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6228
Fc(^)f Ft(z)p Fc(6)p Fu(=)p Ft(y\)")h(by)g(force)634
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6229
1588 y(thus)g("am)q(\(z\)[x:=N][y:=L])j(=)c(am\(z\)[y:=L][x:=N[y:=L]]")
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6230
705 1688 y(using)h(a1)g(a2)g(forget)g(by)g(force)587
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6231
1789 y(next)634 1889 y(case)g(\(2)g(z)f(M)1065 1897 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6232
Fv(1)1100 1889 y Ft(\))h(\(*)f(case)h(2:)g(lambdas)h(*\))634
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6233
1990 y(assume)g(ih:)f("M)1144 1998 y Fv(1)1179 1990 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6234
Ft([x:=N][y:=L])i(=)d(M)1806 1998 y Fv(1)1841 1990 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6235
Ft([y:=L][x:=N[y:=L]]")634 2090 y(assume)i(f1:)f("z)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6236
b Fu(#)g Ft(\(L,N,x,y\)")634 2190 y(from)40 b(f1)g(fresh)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6237
1148 2190 V 29 w(fact1)h(have)f(f2:)g("z)13 b Fu(#)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6238
Ft(N[y:=L]")41 b(by)e(simp)634 2291 y(show)h("\([z].M)1103
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6239
2299 y Fv(1)1139 2291 y Ft(\)[x:=N][y:=L]=\([z].M)1919
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6240
2299 y Fv(1)1959 2291 y Ft(\)[y:=][x:=N[y:=L]]")j(\(is)d("?LHS=?RHS"\))
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6241
634 2391 y(proof)g(-)705 2492 y(have)g("?LHS)g(=)g([z].\(M)1449
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6242
2500 y Fv(1)1485 2492 y Ft([x:=N][y:=L]\)")i(using)f(f1)e(by)h(simp)705
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6243
2592 y(also)g(have)g("...=)h([z].\(M)1567 2600 y Fv(1)1603
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6244
2592 y Ft([y:=L][x:=N[y:=L]]\)")i(using)e(ih)e(by)h(simp)705
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6245
2693 y(also)g(have)g("...=)h(\([z].\(M)1606 2701 y Fv(1)1642
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6246
2693 y Ft([y:=L]\)\)[x:=N[y:=L]]")j(using)c(f1)g(f2)f(by)h(simp)705
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6247
2793 y(also)g(have)g("...=)h(?RHS")f(using)g(f1)g(by)g(simp)705
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6248
2894 y(finally)h(show)f("?LHS)g(=)g(?RHS")g(by)g(simp)634
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6249
2994 y(qed)587 3095 y(next)634 3195 y(case)g(\(3)g(M)987
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6250
3203 y Fv(1)1061 3195 y Ft(M)1100 3203 y Fv(2)1135 3195
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6251
y Ft(\))f(\(*)h(case)g(3:)g(applications)i(*\))634 3295
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6252
y(thus)e("pr)q(\(M)1026 3303 y Fv(1)1061 3295 y Ft(,M)1139
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6253
3303 y Fv(2)1174 3295 y Ft(\)[x:=N][y:=L]=pr)t(\(M)1880
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6254
3303 y Fv(1)1915 3295 y Ft(,M)1993 3303 y Fv(2)2028 3295
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6255
y Ft(\)[y:=L][x:=N[y:=L]]")j(by)d(simp)587 3396 y(qed)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6256
3435 3451 4 2662 v 523 3454 2915 4 v 523 3597 a Fs(Fig.)15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6257
b(3.)27 b Fu(An)g(Isab)r(elle)i(pro)r(of)f(using)g(the)f(Isar)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6258
(language)h(for)g(the)e(substitution)h(lemma)e(sho)n(wn)i(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6259
3689 y(Fig.)j(2.)g(It)e(uses)i(the)e(follo)n(wing)k(auxiliary)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6260
(lemmas:)g Ft(forget)h Fu(whic)n(h)f(states)h(that)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6261
Ft(x)13 b Fu(#)g Ft(L)30 b Fu(implies)523 3780 y Ft(L[x:=T]=L)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6262
Fu(,)23 b(needed)d(in)h(the)f(v)l(ariable)i(case.)f(This)h(case)g(pro)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6263
(ceeds)f(b)n(y)f(stating)h(the)f(three)h(sub)r(cases)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6264
3871 y(to)g(b)r(e)g(considered)g(and)f(then)g(pro)n(ving)g(them)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6265
(automatically)h(using)g(the)f(assumptions)h Ft(a1)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6266
Fu(and)f Ft(a2)p Fu(.)523 3963 y(The)f(lemma)e Ft(fresh)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6267
1114 3963 24 4 v 29 w(fact1)j Fu(in)e(the)g(lam)n(b)r(da-case)g(sho)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6268
(ws)h(from)f Ft(z)13 b Fu(#)g Ft(\(L,N,x,y\))21 b Fu(that)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6269
Ft(z)13 b Fu(#)f Ft(N[x:=L])523 4054 y Fu(holds.)27 b(This)g(lemma)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6270
(is)h(not)f(explicitly)h(men)n(tioned)e(in)i(Barendregt's)h(informal)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6271
(pro)r(of,)h(but)e(it)g(is)523 4145 y(necessary)k(to)g(pull)f(out)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6272
(the)h(substitution)f(from)g(under)g(the)g(binder)g Ft(z)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6273
Fu(.)h(This)g(case)g(pro)r(ceeds)g(as)523 4237 y(follo)n(ws:)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6274
b(the)c(substitutions)h(on)g(left-hand)g(side)g(of)h(the)e(equation)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6275
(can)g(b)r(e)g(mo)n(v)n(ed)e(under)h(the)523 4328 y(binder)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6276
b Ft(z)p Fu(;)g(then)g(one)g(can)h(apply)f(the)f(induction)h(h)n(yp)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6277
(othesis;)h(after)g(this)f(one)h(can)f(pull)g(out)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6278
4419 y(second)e(substitution)f(using)h Ft(z)13 b Fu(#)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6279
Ft(N[y:=L])27 b Fu(and)e(\014nally)h(mo)n(v)n(e)e(out)i(the)f(\014rst)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6280
(substitution)h(using)523 4511 y Ft(z)13 b Fu(#)g Ft(\(L,N,x,y\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6281
Fu(.)28 b(This)e(giv)n(es)g(the)g(righ)n(t-hand)e(side)i(of)h(the)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6282
(equation.)p Black Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6283
%%Page: 15 15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6284
TeXDict begin 15 14 bop Black Black 523 448 a Fx(pro)r(of)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6285
b(through.)h(This)f(incon)n(v)n(enience)g(has)g(b)r(een)i(alleviated)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6286
(b)n(y)h(the)g(v)n(ersion)e(of)i(structural)523 548 y(induction)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6287
b(giv)n(en)f(in)h([8])f(and)g([12],)g(whic)n(h)h(is)f(as)g(follo)n(ws)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6288
984 756 y Fl(9)p Fm(X)r(:)22 b Fe(FINITE)f Fm(X)k Fl(^)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6289
b Fx(\()p Fl(8)j Fm(x)i(t:)f(x)g Fl(62)h Fm(X)g Fl(^)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6290
b Fm(P)35 b(t)23 b Fx(=)-14 b Fl(\))23 b Fm(P)35 b Fx(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6291
Fm(LAM)c(x)24 b(t)p Fx(\)\))523 915 y(F)-7 b(or)35 b(this)h(principle)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6292
(one)f(has)g(to)h(pro)n(vide)f(a)g(\014nite)h(set)g Fm(X)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6293
b Fx(and)36 b(then)g(has)f(to)h(sho)n(w)f(the)523 1014
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6294
y(lam)n(b)r(da-case)28 b(for)i(all)f(binders)h(not)g(in)g(this)g(set.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6295
(This)g(is)g(v)n(ery)f(similar)g(to)h(our)f(induction)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6296
1114 y(principle,)34 b(but)g(w)n(e)f(claim)g(that)h(our)f(v)n(ersion)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6297
(based)h(on)g(freshness)f(\014ts)i(b)r(etter)g(with)g(in-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6298
1214 y(formal)f(practise)h(and)f(can)h(mak)n(e)f(use)h(of)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6299
(infrastructure)e(of)h(Isab)r(elle)g(\(namely)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6300
1313 y(axiomatic)27 b(t)n(yp)r(e-classes)f(enforce)h(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6301
(\014nite-supp)r(ort)f(prop)r(ert)n(y\).)648 1415 y(Lik)n(e)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6302
b(our)h Fm(\003)1026 1427 y Fj(\013)1073 1415 y Fx(,)g(HO)n(AS)h(uses)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6303
(functions)g(to)g(enco)r(de)g(lam)n(b)r(da-abstractions;)e(it)j(comes)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6304
(in)523 1515 y(t)n(w)n(o)18 b(\015a)n(v)n(ours:)f Fo(we)l(ak)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6305
b Fx(HO)n(AS)19 b([4])g(and)f Fo(ful)t(l)29 b Fx(HO)n(AS)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6306
b([15].)h(The)f(adv)-5 b(an)n(tage)18 b(of)h(full)g(HO)n(AS)g(o)n(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6307
(er)523 1614 y(our)24 b(w)n(ork)g(is)h(that)g(notions)f(suc)n(h)h(as)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6308
(capture-a)n(v)n(oiding)e(substitution)k(come)e(for)h(free.)g(W)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6309
b(e,)523 1714 y(on)23 b(the)g(other)g(hand,)g(load)f(the)h(w)n(ork)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6310
(of)h(suc)n(h)f(de\014nitions)i(on)n(to)e(the)h(user.)g(The)g(adv)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6311
b(an)n(tage)523 1814 y(of)36 b(our)g(w)n(ork)f(is)h(that)h(w)n(e)f(ha)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6312
(v)n(e)f(no)h(di\016culties)h(with)g(notions)f(suc)n(h)g(as)f(sim)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6313
(ultaneous-)523 1913 y(substitution)29 b(\(a)f(crucial)f(notion)h(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6314
(the)h(usual)f(strong)f(normalisation)f(pro)r(of)6 b(\),)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6315
b(whic)n(h)f(in)523 2013 y(full)i(HO)n(AS)g(seem)g(rather)e(di\016cult)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6316
j(to)f(enco)r(de.)f(Another)h(adv)-5 b(an)n(tage)28 b(w)n(e)h(see)h(is)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6317
f(that)h(b)n(y)523 2112 y(inductiv)n(ely)f(de\014ning)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6318
Fm(\003)1324 2124 y Fj(\013)1400 2112 y Fx(one)f(has)g(induction)i(for)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6319
e(\\free",)g(whereas)f(induction)i(requires)523 2212
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6320
y(considerable)37 b(e\013ort)i(in)g(full)g(HO)n(AS.)g(The)g(main)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6321
(di\013erence)g(of)f(our)g(w)n(ork)g(with)h(w)n(eak)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6322
2312 y(HO)n(AS)32 b(is)g(that)g(w)n(e)g(use)g Fo(some)39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6323
b Fx(sp)r(eci\014c)32 b(functions)h(to)f(represen)n(t)e(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6324
(da-abstractions;)523 2411 y(in)22 b(con)n(trast,)e(w)n(eak)h(HO)n(AS)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6325
(uses)h(the)g Fo(ful)t(l)31 b Fx(function)22 b(space.)f(This)g(causes)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6326
(problems)g(kno)n(wn)523 2511 y(b)n(y)27 b(the)h(term)g(\\exotic)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6327
(terms"|essen)n(tially)e(junk)j(in)g(the)g(mo)r(del.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6328
2788 y Fp(7)112 b(Conclusion)523 2998 y Fx(The)37 b(pap)r(er)f([2],)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6329
(whic)n(h)h(sets)f(out)h(some)f(c)n(hallenges)f(for)h(automated)g(pro)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6330
(of)g(assistan)n(ts,)523 3098 y(claims)18 b(that)h(theorem)g(pro)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6331
(ving)e(tec)n(hnologies)g(ha)n(v)n(e)h(almost)g(reac)n(hed)f(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6332
(threshold)g(where)523 3198 y(they)36 b(can)f(b)r(e)i(used)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6333
Fo(by)j(the)f(masses)43 b Fx(for)36 b(formal)f(reasoning)e(ab)r(out)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6334
(programming)e(lan-)523 3297 y(guages.)d(W)-7 b(e)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6335
b(hop)r(e)f(to)f(ha)n(v)n(e)g(pushed)h(with)h(this)f(pap)r(er)f(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6336
(b)r(oundary)e(of)h(the)g(state-of-)523 3397 y(the-art)i(in)h(formal)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6337
(reasoning)f(closer)h(to)h(this)g(threshold.)f(W)-7 b(e)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6338
b(sho)n(w)n(ed)f(all)h(our)f(results)523 3497 y(for)e(the)h(lam)n(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6339
(da-calculus.)f(But)h(the)g(lam)n(b)r(da-calculus)e(is)h(only)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6340
Fo(one)40 b Fx(example.)33 b(W)-7 b(e)34 b(en-)523 3596
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6341
y(visage)e(no)g(problems)g(generalising)f(our)h(results)h(to)g(other)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6342
(term-calculi.)g(In)h(fact,)g(there)523 3696 y(is)e(already)e(w)n(ork)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6343
(b)n(y)i(Bengtson)f(adapting)g(our)g(results)g(to)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6344
Fm(\031)s Fx(-calculus.)f(W)-7 b(e)32 b(also)d(do)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6345
3795 y(not)k(en)n(visage)e(problems)i(with)g(pro)n(viding)f(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6346
(general)e(framew)n(ork)g(for)i(reasoning)e(ab)r(out)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6347
3895 y(binders)26 b(based)g(on)h(our)f(results.)g(The)h(real)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6348
(\(implemen)n(tation\))j(c)n(hallenge)d(is)i(to)f(in)n(tegrate)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6349
3995 y(these)f(results)f(in)n(to)h(Isab)r(elle's)g(datat)n(yp)r(e)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6350
(pac)n(k)-5 b(age)24 b(so)g(that)h(the)g(user)g(do)r(es)f(not)h(see)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6351
(an)n(y)f(of)523 4094 y(the)j(tedious)e(details)h(through)g(whic)n(h)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6352
(w)n(e)f(had)h(to)g(go.)g(F)-7 b(or)25 b(example)h(one)f(w)n(ould)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6353
(lik)n(e)g(that)523 4194 y(the)31 b(subset)f(construction)g(from)g(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6354
(bigger)e(set)h(is)h(done)f(completely)g(b)r(ehind)i(the)f(scenes.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6355
4294 y(Deriving)24 b(an)g(induction)h(principle)f(should)g(also)f(b)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6356
(e)i(done)f(automatically)-7 b(.)24 b(Ideally)-7 b(,)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6357
b(a)g(user)523 4393 y(just)33 b(de\014nes)f(an)g(inductiv)n(e)g(datat)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6358
(yp)r(e)g(and)g(indicates)g(where)f(binders)h(are|the)f(rest)h(of)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6359
4493 y(the)24 b(infrastructure)e(should)i(b)r(e)f(pro)n(vided)g(b)n(y)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6360
(the)h(theorem)f(pro)n(v)n(er.)e(This)i(is)h(future)f(w)n(ork.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6361
4649 y Ff(Ac)m(kno)m(wledgemen)m(ts:)39 b Fx(The)i(\014rst)g(author)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6362
(is)h(v)n(ery)f(grateful)g(to)h(Andrew)g(Pitts)g(and)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6363
4749 y(Mic)n(hael)25 b(Norrish)g(for)g(the)h(man)n(y)f(discussions)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6364
(with)h(them)g(on)g(the)g(sub)5 b(ject)26 b(of)f(the)h(pap)r(er.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6365
4848 y(W)-7 b(e)36 b(thank)g(James)f(Cheney)-7 b(,)36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6366
b(Aaron)f(Bohannon,)g(Daniel)h(W)-7 b(ang)35 b(and)h(one)g(anon)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6367
(ymous)523 4948 y(referee)27 b(for)g(their)h(suggestions.)e(The)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6368
(\014rst)g(author's)f(in)n(terest)g(in)h(this)g(w)n(ork)f(w)n(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6369
(spark)n(ed)p Black Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6370
%%Page: 16 16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6371
TeXDict begin 16 15 bop Black Black 523 448 a Fx(b)n(y)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6372
b(an)g(email-discussion)e(with)j(F)-7 b(rank)29 b(Pfenning)h(and)g(b)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6373
(y)g(a)f(question)h(from)g(Neil)g(Ghani)523 548 y(at)e(the)g(spring)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6374
(sc)n(ho)r(ol)h(of)g(Midland)h(Graduate)f(Sc)n(ho)r(ol.)g(The)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6375
(Alexander-v)n(on-Hum)n(b)r(oldt)523 648 y(F)-7 b(oundation)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6376
b(funded)i(the)f(\014rst)f(author.)523 913 y Fp(References)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6377
Black 561 1104 a Fu(1.)p Black 43 w(T.)e(Altenkirc)n(h.)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6378
b(A)25 b(Formalization)h(of)f(the)g(Strong)f(Normalisation)i(Pro)r(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6379
(for)g(System)d(F)i(in)663 1196 y(LEGO.)34 b(In)25 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6380
Fq(Pr)l(o)l(c.)j(of)f(TLCA)p Fu(,)f(v)n(olume)f(664)i(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6381
Fq(LNCS)p Fu(,)g(pages)h(13{28,)h(1993.)p Black 561 1287
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6382
a(2.)p Black 43 w(B.)i(E.)f(Aydemir,)f(A.)h(Bohannon,)h(M.)g(F)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6383
b(airbairn,)30 b(J.)g(N.)g(F)-6 b(oster,)30 b(B.)g(C.)g(Pierce,)g(P)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6384
b(.)30 b(Sew)n(ell,)663 1378 y(D.)21 b(Vytiniotis,)h(G.)g(W)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6385
b(ash)n(burn,)20 b(S.)h(W)-6 b(eiric)n(h,)22 b(and)f(S.)g(Zdancewic.)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6386
b(Mec)n(hanized)22 b(Metatheory)663 1469 y(for)k(the)f(Masses:)j(The)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6387
(PoplMark)h(Challenge.)g(accepted)f(at)g(tphol)f(05.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6388
Black 561 1561 a(3.)p Black 43 w(H.)33 b(Barendregt.)58
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6389
b Fq(The)35 b(Lamb)l(da)g(Calculus:)g(Its)f(Syntax)j(and)e(Semantics)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6390
Fu(,)f(v)n(olume)f(103)h(of)663 1652 y Fq(Studies)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6391
b(in)f(L)l(o)l(gic)h(and)g(the)h(F)-6 b(oundations)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6392
b(of)e(Mathematics)p Fu(.)36 b(North-Holland,)26 b(1981.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6393
Black 561 1743 a(4.)p Black 43 w(J.)21 b(Desp)r(eyroux,)f(A.)g(F)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6394
b(elt)n(y)g(,)20 b(and)g(A.)g(Hirsc)n(ho)n(witz.)27 b(Higher-Order)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6395
b(Abstract)g(Syn)n(tax)f(in)h(Co)r(q.)663 1835 y(In)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6396
b Fq(Pr)l(o)l(c.)j(of)f(TLCA)p Fu(,)f(v)n(olume)e(902)j(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6397
Fq(LNCS)p Fu(,)g(pages)h(124{138,)i(1995.)p Black 561
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6398
1926 a(5.)p Black 43 w(M.)e(J.)g(Gabba)n(y)-6 b(.)37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6399
b Fq(A)28 b(The)l(ory)h(of)f(Inductive)i(De\014nitions)f(With)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6400
Fr(\013)p Fq(-e)l(quivalenc)l(e)p Fu(.)39 b(PhD)26 b(thesis,)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6401
2017 y(Univ)n(ersit)n(y)e(of)j(Cam)n(bridge,)f(2000.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6402
Black 561 2109 a(6.)p Black 43 w(M.)d(J.)h(Gabba)n(y)f(and)f(A.)h(M.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6403
(Pitts.)31 b(A)22 b(New)h(Approac)n(h)g(to)g(Abstract)g(Syn)n(tax)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6404
(with)i(Variable)663 2200 y(Binding.)34 b Fq(F)-6 b(ormal)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6405
b(Asp)l(e)l(cts)i(of)d(Computing)p Fu(,)g(13:341{363,)i(2001.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6406
Black 561 2291 a(7.)p Black 43 w(J.-Y.)f(Girard,)g(Y.)g(Lafon)n(t,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6407
(and)e(P)-6 b(.)28 b(T)-6 b(a)n(ylor.)41 b Fq(Pr)l(o)l(ofs)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6408
b(and)g(Typ)l(es)p Fu(,)f(v)n(olume)e(7)h(of)g Fq(Cambridge)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6409
2383 y(T)-6 b(r)l(acts)29 b(in)e(The)l(or)l(etic)l(al)i(Computer)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6410
(Scienc)l(e)p Fu(.)35 b(Cam)n(bridge)26 b(Univ)n(ersit)n(y)e(Press,)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6411
(1989.)p Black 561 2474 a(8.)p Black 43 w(A.)21 b(D.)g(Gordon.)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6412
b(A)21 b(Mec)n(hanisation)i(of)f(Name-Carrying)f(Syn)n(tax)f(up)g(to)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6413
(Alpha-Con)n(v)n(ersion.)663 2565 y(In)28 b Fq(Pr)l(o)l(c.)i(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6414
(Higher-or)l(der)j(lo)l(gic)d(the)l(or)l(em)i(pr)l(oving)f(and)g(its)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6415
(applic)l(ations)p Fu(,)g(v)n(olume)d(780)j(of)663 2657
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6416
y Fq(LNCS)p Fu(,)c(pages)g(414{426,)j(1993.)p Black 561
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6417
2748 a(9.)p Black 43 w(A.)35 b(D.)h(Gordon)g(and)g(T.)g(Melham.)64
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6418
b(Fiv)n(e)36 b(Axioms)f(of)i(Alpha-Con)n(v)n(ersion.)64
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6419
b(In)35 b Fq(Pr)l(o)l(c.)i(of)663 2839 y(TPHOL)p Fu(,)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6420
b(v)n(olume)g(1125)i(of)g Fq(LNCS)p Fu(,)f(pages)g(173{190,)j(1996.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6421
Black 523 2931 a(10.)p Black 43 w(D.)e(Hirsc)n(hk)n(o\013.)40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6422
b(A)28 b(Full)g(F)-6 b(ormalisation)29 b(of)f Fr(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6423
Fu(-Calculus)g(Theory)g(in)g(the)f(Calculus)i(of)g(Con-)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6424
3022 y(structions.)35 b(In)25 b Fq(Pr)l(o)l(c.)j(of)f(TPHOL)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6425
Fu(,)f(v)n(olume)e(1275)j(of)g Fq(LNCS)p Fu(,)f(pages)g(153{169,)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6426
(1997.)p Black 523 3113 a(11.)p Black 43 w(T.)k(Nipk)n(o)n(w,)f(L.)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6427
(C.)g(P)n(aulson,)g(and)f(M.)h(W)-6 b(enzel.)54 b Fq(Isab)l(el)t(le)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6428
b(HOL:)f(A)g(Pr)l(o)l(of)h(Assistant)i(for)663 3205 y(Higher-Or)l(der)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6429
29 b(Lo)l(gic)p Fu(,)e(v)n(olume)d(2283)j(of)g Fq(LNCS)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6430
Fu(.)34 b(Springer-V)-6 b(erlag,)26 b(2002.)p Black 523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6431
3296 a(12.)p Black 43 w(M.)f(Norrish.)34 b(Mec)n(hanising)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6432
b Fr(\025)p Fu(-calculus)f(using)h(a)f(Classical)j(First)e(Order)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6433
(Theory)h(of)h(Terms)663 3387 y(with)g(Perm)n(utations,)f(forthcoming.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6434
p Black 523 3479 a(13.)p Black 43 w(M.)34 b(Norrish.)60
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6435
b(Recursiv)n(e)34 b(Function)g(De\014nition)g(for)h(Typ)r(es)f(with)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6436
(Binders.)60 b(In)34 b Fq(Pr)l(o)l(c.)h(of)663 3570 y(TPHOL)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6437
Fu(,)25 b(v)n(olume)g(3223)i(of)g Fq(LNCS)p Fu(,)f(pages)g(241{256,)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6438
(2004.)p Black 523 3661 a(14.)p Black 43 w(L.)c(P)n(aulson.)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6439
b(De\014ning)25 b(F)-6 b(unctions)26 b(on)f(Equiv)l(alence)h(Classes.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6440
36 b(T)-6 b(o)26 b(app)r(ear)g(in)f(A)n(CM)h(T)-6 b(rans-)663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6441
3753 y(actions)26 b(on)g(Computational)g(Logic.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6442
523 3844 a(15.)p Black 43 w(F.)k(Pfenning)g(and)f(C.)h(Elliott.)47
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6443
b(Higher-Order)29 b(Abstract)h(Syn)n(tax.)44 b(In)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6444
b Fq(Pr)l(o)l(c.)j(of)e(the)i(A)n(CM)663 3935 y(SIGPLAN)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6445
b(Confer)l(enc)l(e)i(PLDI)p Fu(,)d(pages)g(199{208.)j(A)n(CM)d(Press,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6446
(1989.)p Black 523 4027 a(16.)p Black 43 w(A.)g(M.)i(Pitts.)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6447
b(Nominal)27 b(Logic,)i(A)f(First)g(Order)g(Theory)g(of)h(Names)e(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6448
(Binding.)42 b Fq(Infor-)663 4118 y(mation)27 b(and)h(Computation)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6449
Fu(,)g(186:165{193,)i(2003.)p Black 523 4209 a(17.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6450
Black 43 w(A.)18 b(S.)h(T)-6 b(ro)r(elstra)21 b(and)e(H.)f(Sc)n(h)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6451
(wic)n(h)n(ten)n(b)r(erg.)23 b Fq(Basic)f(Pr)l(o)l(of)g(The)l(ory)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6452
Fu(,)e(v)n(olume)e(43)i(of)f Fq(Cambridge)663 4301 y(T)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6453
b(r)l(acts)29 b(in)e(The)l(or)l(etic)l(al)i(Computer)g(Scienc)l(e)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6454
Fu(.)35 b(Cam)n(bridge)26 b(Univ)n(ersit)n(y)e(Press,)j(2000.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6455
Black 523 4392 a(18.)p Black 43 w(C.)f(Urban,)g(A.)g(M.)h(Pitts,)g(and)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6456
f(M.)g(J.)h(Gabba)n(y)-6 b(.)35 b(Nominal)26 b(Uni\014cation.)35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6457
b Fq(The)l(or)l(etic)l(al)30 b(Com-)663 4483 y(puter)f(Scienc)l(e)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6458
Fu(,)e(323\(1-2\):473{497,)j(2004.)p Black 523 4575 a(19.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6459
Black 43 w(M.)21 b(V)-6 b(anIn)n(w)n(egen.)25 b Fq(The)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6460
(Machine-Assiste)l(d)h(Pr)l(o)l(of)e(of)g(Pr)l(o)l(gr)l(amming)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6461
(Language)g(Pr)l(op)l(erties)p Fu(.)663 4666 y(PhD)h(thesis,)h(Univ)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6462
(ersit)n(y)f(of)i(P)n(ennsylv)l(ania,)e(1996.)36 b(Av)l(ailable)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6463
b(as)h(MS-CIS-96-31.)p Black 523 4757 a(20.)p Black 43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6464
w(M.)38 b(W)-6 b(enzel.)69 b Fq(Using)38 b(Axiomatic)h(Typ)l(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6465
(Classes)g(in)f(Isab)l(el)t(le)p Fu(.)70 b(Man)n(ual)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6466
b(in)f(the)g(Isab)r(elle)663 4848 y(distribution.)p Black
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6467
Black eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6468
%%Trailer
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6469
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6470
userdict /end-hook known{end-hook}if
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  6471
%%EOF