  In a finite volume system, we prove a no-go theorem on a Leibniz rule with a
care of locality argument on latttice. The new possibility on the Leibniz rule
solutions on lattice is discussed. Although the new solution admits a local
difference operator, a non-local product rule is needed. In the case, a
supersymmetric interacting theory is simply realized. The difference between
finite flavor systems and matrix representations of infinite flavor systems is
explained based on a finite volume system analysis including the no-go theorem.
