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;

theorem
  (line_homography(N)).l1 = (line_homography(N)).l2 implies l1 = l2
  proof
    assume (line_homography(N)).l1 = (line_homography(N)).l2;
    then l1 = (line_homography(N~)).((line_homography(N)).l2) by Th15
           .= l2 by Th15;
    hence thesis;
  end;
