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
  for h,g being Element of GroupLineHomography3
  for N,Ng being invertible Matrix of 3,F_Real st
  h = line_homography(N) & g = line_homography(Ng) & Ng = N~
  holds g = h"
  proof
    let h,g be Element of GLH3;
    let N,Ng be invertible Matrix of 3,F_Real;
    assume h = line_homography(N) & g = line_homography(Ng) & Ng = N~;
    then h * g = 1_GLH3 & g * h = 1_GLH3 by Lm2,Th18;
    hence g = h" by GROUP_1:def 5;
  end;
