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A formal proof of Sylow’s theorem. An experiment in abstract algebra with Isabelle H0L. (English) Zbl 0943.68149
Summary: The theorem of Sylow is proved in Isabelle H0L. We follow the proof by Wielandt that is more general than the original and uses a nontrivial combinatorial identity. The mathematical proof is explained in some detail, leading on to the mechanization of group theory and the necessary combinatorics in Isabelle. We present the mechanization of the proof in detail, giving reference to theorems contained in an appendix. Some weak points of the experiment with respect to a natural treatment of abstract algebraic reasoning give rise to a discussion of the use of module systems to represent abstract algebra in theorem provers. Drawing from that, we present tentative ideas for further research into a section concept for Isabelle.
MSC:
68T15Theorem proving (deduction, resolution, etc.)
03B35Mechanical theorem proving; logical operations
20E07Subgroup theorems; subgroup growth
20-04Machine computation, programs (group theory)
Keywords:
Isabelle HOL
Software:
Isabelle