theorem
  for h,g being Element of GroupHomography3
  for N,Ng being invertible Matrix of 3,F_Real st
  h = homography(N) & g = homography(Ng) & Ng = N~
  holds g = h"
  proof
    let h,g be Element of GH3;
    let N,Ng be invertible Matrix of 3,F_Real;
    assume h = homography(N) & g = homography(Ng) & Ng = N~;
    then h * g = 1_GH3 & g * h = 1_GH3 by Lm2,Ta2;
    hence g = h" by GROUP_1:def 5;
  end;
