  The Discounted Least Information Theory of Entropy (DLITE) is a new
information measure that quantifies the amount of entropic difference between
two probability distributions. It manifests multiple critical properties both
as an information-theoretic quantity and as metric distance. In the report, we
provide a proof of the triangular inequality of DLITE's cube root
($\sqrt[3]{DL}$), an important property of a metric, along with alternative
proofs for two additional properties.
