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arXiv · 1503.02349

Arithmetic in Metamath, Case Study: Bertrand's Postulate

Mario Carneiro
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Abstract

Unlike some other formal systems, the proof system Metamath has no built-in concept of "decimal number" in the sense that arbitrary digit strings are not recognized by the system without prior definition. We present a system of theorems and definitions and an algorithm to apply these as basic operations to perform arithmetic calculations with a number of steps proportional to an arbitrary-precision arithmetic calculation. We consider as case study the formal proof of Bertrand's postulate, which required the calculation of many small primes. Using a Mathematica implementation, we were able to complete the first formal proof in Metamath using numbers larger than 10. Applications to the mechanization of Metamath proofs are discussed, and a heuristic argument for the feasability of large proofs such as Tom Hales' proof of the Kepler conjecture is presented.

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Mario Carneiro. 2015-03-09. Arithmetic in Metamath, Case Study: Bertrand's Postulate. https://arxiv.org/abs/1503.02349

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