 The main difference between \((\CP_w )\) and \((\CP_n )\) is that on \((\CP_w )\), there are two ways of discharging your obligation: by doing \(X\) or by making it the case that \(C\) is not fulfilled. Not so on \((\CP_n )\): once \(C\) is fulfilled, you must do \(X\). Only on \((\CP_n )\), that is, can the consequent be detached.