  An obstacle to realize supersymmetry on a lattice is the breakdown of Leibniz
rule. We give a proof of a no-go theorem that it is impossible to construct a
lattice field theory in an infinite lattice volume with any nontrivial field
products and difference operators that satisfy the following three properties:
(i) translation invariance, (ii) locality and (iii) Leibniz rule. We then
propose a way to escape from the no-go theorem by introducing infinite flavors,
and present a lattice model of N=2 supersymmetric quantum mechanics equipped
with the full exact supersymmetry.
