reserve P for Element of BK_model;

theorem
  ex P1,P2 being Element of absolute st
  P1 <> P2 & P1,P,P2 are_collinear
  proof
    consider Q be Element of BK_model such that
A1: P <> Q by Th11;
    consider P1,P2 be Element of absolute such that
A2: P1 <> P2 and
A3: P,Q,P1 are_collinear and
A4: P,Q,P2 are_collinear by A1,BKMODEL2:20;
    take P1,P2;
    P,P1,P2 are_collinear by A1,A3,A4,COLLSP:6;
    hence thesis by A2,COLLSP:4;
  end;
