 Looking to the fifth \(\APUL\) reduction axiom, the conjunct \(\bigwedge_{e\gt_a f}K_a[A,f]G\) says that G is true whenever an event of plausibility strictly greater than e is applied to a world within a’s current connected component. This tells us that G is true at worlds having greater plausibility in light of the first bulleted item above. The other conjunct \(\bigwedge_{e\simeq_a f}\Box_a[A,f]G)\) of the fifth \(\APUL\) reduction axiom says that G is true whenever an event equi-plausible with e is applied to world of equal or greater plausibility within a’s current connected component. This tells us that G is true at worlds having greater or equal plausibility in light of the second bulleted item above. Taken together, since these two bulleted items define when it is that a world has equal or greater plausibility in the resultant model \(M[A]\), the truth of these two conjuncts at an initial situation \((M,w)\) at which \((A,e)\) is executable implies that G is true at all worlds of equal or greater plausibility than the actual world \((w,e)\) of the resultant model \(M[A]\). That is, we have \(M[A],(w,e)\models\Box_a G\) and therefore that \(M,w\models[A,e]G\). This explains the right-to-left direction of the fifth \(\APUL\) reduction axiom. The left-to-right direction is explained similarly. 