reserve AFP for AffinPlane;
reserve a,a9,b,b9,c,c9,d,d9,o,p,p9,q,q9,r,s,t,x,y,z for Element of AFP;
reserve A,A9,C,D,P,B9,M,N,K for Subset of AFP;
reserve f for Permutation of the carrier of AFP;

theorem
  AFP is Desarguesian iff for o,a,b st o<>a & o<>b & LIN o,a,b ex f st f
  is dilatation & f.o=o & f.a=b by Th2,Th3;
