  We provide a sufficient condition for the monogamy inequality of multi-party
quantum entanglement of arbitrary dimensions in terms of entanglement of
formation. Based on the classical-classical-quantum(ccq) states whose quantum
parts are obtained from the two-party reduced density matrices of a three-party
quantum state, we show the additivity of the mutual information of the ccq
states guarantees the monogamy inequality of the three-party pure state in
terms of EoF. After illustrating the result with some examples, we generalize
our result of three-party systems into any multi-party systems of arbitrary
dimensions.
