 According to the product update, we insert an a-arrow \((v_1,f_1)\to_a (v_2,f_2)\) in \(M[A]\) if and only if there is an a-arrow \(v_1\to_a v_2\) in M and an a-arrow \(f_1\to_a f_2\) in A. In this way, agent a’s uncertainty in the resultant model \(M[A]\) comes from two sources: her initial uncertainty in M (represented by \(R^M_a\)) as to which is the actual world and her uncertainty in A (represented by \(R^A_a\)) as to which is the actual event. Finally, the valuation at the copy \((v,f)\) in \(M[A]\) is just the same as it was at the original world v in M. 