  When combined with the results of D1 and D2 (or, alternatively, with the results of D3 and D4), this result entails that Purity-F is in fact false. To see this, recall that D1 and D2 (as well as D3 and D4) together entail that if the one is, then Purity-F is false. Now, by D5, if the one is not, then Purity-F is false. So, whether the one is or is not, Purity-F is false. So Purity-F is false.