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 Th59:
  X is being_plane implies X <> {}
proof
  assume X is being_plane;
  then ex a,b,c st a in X & b in X & c in X & not LIN a,b,c by Th34;
  hence thesis;
end;
