We present an original theorem in auction theory: it specifies general
conditions under which the sum of the payments of all bidders is necessarily
not identically zero, and more generally not constant. Moreover, it explicitly
supplies a construction for a finite minimal set of possible bids on which such
a sum is not constant. In particular, this theorem applies to the important
case of a second-price Vickrey auction, where it reduces to a basic result of
which a novel proof is given. To enhance the confidence in this new theorem, it
has been formalized in Isabelle/HOL: the main results and definitions of the
formal proof are re- produced here in common mathematical language, and are
accompanied by an informal discussion about the underlying ideas.Comment: 6th Podlasie Conference on Mathematics 2014, 11 page