 The theorem itself does not require the full apparatus of Bayesian probability functions. It draws only on likelihoods. Neither the statement of the theorem nor its proof employ prior probabilities of any kind. So even likelihoodists, who eschew the use of Bayesian prior probabilities, may embrace this result. Given the forms of Bayes’ Theorem, 9*-11 from the previous section, the Likelihood Ratio Convergence Theorem further implies the likely convergence to 0 of the posterior probabilities of false competitors of a true hypothesis. That is, when the ratios \(P[e^n \pmid h_{j}\cdot b\cdot c^{n}] / P[e^n \pmid h_{i}\cdot b\cdot c^{n}]\) approach 0 for increasing n, the Ratio Form of Bayes’ Theorem,  Equation 9*,  says that the posterior probability of \(h_j\) must also approach 0 as evidence accumulates, regardless of the value of its prior probability. So, support functions in collections representing vague prior plausibilities for an individual agent (i.e., a vagueness set) and representing the diverse range of priors for a community of agents (i.e., a diversity set) will come to agree on the near 0 posterior probability of empirically distinct false rivals of a true hypothesis. And as the posterior probabilities of false competitors fall, the posterior probability of the true hypothesis heads towards 1. Thus, the theorem establishes that the inductive logic of probabilistic support functions satisfies the  Criterion of Adequacy (CoA)  suggested at the beginning of this article.