
theorem Th58:
  for P,Q being Element of BK_model st P <> Q holds
  ex R being Element of absolute st
  (for p,q,r being non point_at_infty Element of ProjectiveSpace TOP-REAL 3 st
  p = P & q = Q & r = R holds between RP3_to_T2 p,RP3_to_T2 q,RP3_to_T2 r)
  proof
    let P,Q be Element of BK_model;
    assume P <> Q;
    then consider R be Element of absolute such that
A1: (for p,q,r being non point_at_infty Element of ProjectiveSpace TOP-REAL 3
      st p = Q & q = P & r = R holds
      between RP3_to_T2 q,RP3_to_T2 p,RP3_to_T2 r) by Th57;
    take R;
    thus thesis by A1;
  end;
