 It is a theorem of the probability calculus that \(\Pr(H|E) \leq \Pr(E\rightarrow H)\). So if \(H\) is assigned a high degree of belief given \(E\), the material conditional \(E\rightarrow H\) must have been assigned a degree of belief at least as high ex ante. It is easy to see that as a probabilistic analogue of the principle of Conditionalization from non-monotonic logic or, equivalently, the AGM Inclusion principle. That observation has the following consequence: any belief that the Lockean comes to have after conditioning, she could have arrived at by adding the evidence to her prior beliefs and closing under logical consequence. Therefore Lockean updating satisfies the AGM principle of Inclusion. Furthermore, it follows immediately from definitions that Lockean update satisfies Success and Extensionality.