reserve P for Element of BK_model;

theorem
  for Q being Element of absolute holds
  ex R being Element of BK_model st P <> R & P,Q,R are_collinear
  proof
    let Q be Element of absolute;
    reconsider P1 = P,Q1 = Q as Element of real_projective_plane;
    consider R1 be Element of real_projective_plane such that
A1: R1 in BK_model and
A2: P1 <> R1 and
A3: R1,P1,Q1 are_collinear by BKMODEL2:22;
    reconsider R = R1 as Element of BK_model by A1;
    take R;
    thus thesis by A3,A2,HESSENBE:1;
  end;
