 reserve i,n for Nat;
 reserve r for Real;
 reserve ra for Element of F_Real;
 reserve a,b,c for non zero Element of F_Real;
 reserve u,v for Element of TOP-REAL 3;
 reserve p1 for FinSequence of (1-tuples_on REAL);
 reserve pf,uf for FinSequence of F_Real;
 reserve N for Matrix of 3,F_Real;
 reserve K for Field;
 reserve k for Element of K;
 reserve N,N1,N2 for invertible Matrix of 3,F_Real;
 reserve P,P1,P2,P3 for Point of ProjectiveSpace TOP-REAL 3;

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;
