There is a unique crossing-minimal rectilinear drawing of K_18

We show that, up to order type isomorphism, there is a unique crossing-minimal rectilinear drawing of K18. It is easily verified that this drawing does not contain any crossing-minimal drawing of K17. Therefore this settles, in the negative, the following question from Aichholzer and Krasser: is it true that, for every integer n ≥ 4, there exists a crossing-minimal drawing of Kn that contains a crossing-minimal drawing of Kn − 1?