 But since \(A\) is compatible with \(K\), \(K+A \subseteq K*A\), by (\(*\)4). So both \(\neg A &gt; B\) and \(\neg A &gt; C\) are in \(K*A\). This implies, by GRT again, that both \(B\) and \(C\) are in \((K*A)*\neg A\). Since \(B\) and \(C\) are inconsistent with each other, the latter belief set is inconsistent, contradicting (\(*\)5). So the supposition is impossible.