The MDG system is a decision diagram based verification tool, primarily designed for hardware verification. It is based on Multiway decision diagrams---an extension of the traditional ROBDD approach. In this paper we describe the formal verification of the component library of the MDG system, using HOL. The hardware component library, whilst relatively simple, has been a source of errors in an earlier developmental version of the MDG system. Thus verifying these aspects is of real utility towards the verification of a decision digram based verification system. This work demonstrates how machine assisted proof can be of practical utility when applied to a small focused problem.