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Interesting algorithms in the formalization of the Feit-Thompson theorem?

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It looks like George Gonthier and his collaborators have finished formalizing the Odd Order Theorem.

In his earlier work on the Four Color Theorem, Gonthier invented a bunch of new algorithms (mostly variants of BDDs and graph algorithms) which were especially amenable to formal verification. Since he has said that he was continuing to use this small-scale reflection style of verification in the work on finite group theory, I wonder what new algorithmic tricks were developed during this development?


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