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
  not K is being_line implies Plane(K,P) = {}
proof
  assume
A1: not K is being_line;
  set x = the Element of Plane(K,P);
  assume Plane(K,P)<>{};
  then x in Plane(K,P);
  then ex a st x=a & ex b st a,b // K & b in P;
  hence contradiction by A1,AFF_1:26;
end;
