A Machine-Checked Proof of the Odd Order Theorem - Gonthier, Georges; Asperti, Andrea; Avigad, Jeremy; Bertot, Yves; Cohen, Cyril; Garillot, François; Roux, Stéphane Le; Mahboubi, Assia; O'Connor, Russell; Biha, Sidi Ould; Pasca, Ioana; Rideau, Laurence; et al. (Interactive Theorem Proving, 2013)
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.