reserve AS for AffinSpace;
reserve a,b,c,d,a9,b9,c9,d9,p,q,r,x,y for Element of AS;
reserve A,C,K,M,N,P,Q,X,Y,Z for Subset of AS;

theorem
  AS is not AffinPlane implies AS is Desarguesian
proof
  assume AS is not AffinPlane;
  then
  for A,P,C,q,a,b,c,a9,b9,c9 holds q in A & q in P & q in C & q<>a & q<>b
  & q<>c & a in A & a9 in A & b in P & b9 in P & c in C & c9 in C & A is
being_line & P is being_line & C is being_line & A<>P & A<>C & a,b // a9,b9 & a
  ,c // a9,c9 implies b,c // b9,c9 by Th49;
  hence thesis by AFF_2:def 4;
end;
