reserve P for Element of BK_model;
reserve N,N1,N2 for invertible Matrix of 3,F_Real;
reserve l,l1,l2 for Element of the Lines of IncProjSp_of real_projective_plane;
reserve P for Point of ProjectiveSpace TOP-REAL 3,
        l for LINE of IncProjSp_of real_projective_plane;

theorem
  BK-model-Plane is satisfying_CongruenceSymmetry
  proof
    let P,Q be POINT of BK-model-Plane;
    ex h be Element of SubGroupK-isometry,
      N be invertible Matrix of 3,F_Real st
      h = homography(N) & homography(N).P = Q &
      homography(N).Q = P by BKMODEL2:60;
    hence P,Q equiv Q,P by Def05;
  end;
