Abstract

The Flyspeck project [3] has as its goal the complete formalization of Hales’ proof [2] of the Kepler conjecture. The formalization has to be carried out within a mechanical theorem prover. For our work described in this paper, we have chosen the generic proof assistant Isabelle, tailored to Higher-Order Logic (HOL) [4]. In the following, we will refer to this environment as Isabelle/HOL. An important step in Hales ’ proof is the maximization of about 10 5 real linear programs. The size of these linear programs (LPs) varies, the largest among them consist of about 2000 inequalities in about 200 variables. The considered LPs have the important property that there exist a priori bounds on the range of the variables. The situation is further simplified by our attitude towards the linear programs: we only want to know wether the objective function of a given LP is bounded from above by a given constant K. Under these assumptions, Hales describes [1] a method for obtaining an arbitrarily precise upper bound for the maximum value of the objective function of an LP. This method still works nicely in the context of mechanical theorem

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