In order to update a context with (31), we must do the equivalent of updating with (32a). Now clause (ii) says that to update a context with (32a), we must first try updating with (32b), and subtract the result from the original context (so as to leave behind whichever worlds are not compatible with (32a)). But (32b) is a conjunction, so we must first update with the left conjunct (32c), and then with the right (32d). Updating with (32c) is only defined if the presupposition that there is a king is satisfied in all worlds in the context set. We immediately see that (31) and (32a), (32b), and (32c) all have this requirement, i.e., they presuppose that there is a king. Provided this presupposition is satisfied, updating with (32c) produces a subset of worlds where the king is angry. We use this reduced context set for update with (32d). But update with (32d) again uses the negation clause (ii) of the above definition. So we started off with a set of worlds where there is a king, we reduced it to a set of worlds where the king is angry, and now we must update that context with (32e), an update which will only be defined if there is a knave.