  In this paper we show that in systems where the probability distribution of
the the overlap is non trivial in the infinity volume limit, the property of
ultrametricity can be proved in general starting from two very simple and
natural assumptions: each replica is equivalent to the others (replica
equivalence or stochastic stability) and all the mutual information about a
pair of equilibrium configurations is encoded in their mutual distance or
overlap (separability or overlap equivalence).
