A machine-checked proof of the odd order theorem

Authors:
Georges Gonthier;Andrea Asperti;Jeremy Avigad;Yves Bertot;Cyril Cohen;François Garillot;Stéphane Le Roux;Assia Mahboubi;Russell O'Connor;Sidi Ould Biha;Ioana Pasca;Laurence Rideau;Alexey Solovyev;Enrico Tassi;Laurent Théry
Affiliations:
Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France;Microsoft Research - Inria Joint Centre, France
Venue:
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Year:
2013

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Abstract

This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework implemented by Coq. To support the formalization, we developed a comprehensive set of reusable libraries of formalized mathematics, including results in finite group theory, linear algebra, Galois theory, and the theories of the real and complex algebraic numbers.