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_CongruenceIdentity
  proof
    let P,Q,R be Point of BK-model-Plane;
    assume P,Q equiv R,R;
    then ex h being Element of SubGroupK-isometry st
    ex N being invertible Matrix of 3,F_Real st
    h = homography(N) & homography(N).P = R & homography(N).Q = R by Def05;
    hence P = Q by BKMODEL2:62;
  end;
