 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 a being non zero Element of F_Real
  holds (homography(a*N1)).P = (homography(N1)).P
  proof
    let a be non zero Element of F_Real;
    set M = a * 1.(F_Real,3);
    thus (homography(a*N1)).P = (homography(M * N1)).P by Th02
                      .= (homography(M)).((homography(N1)).P) by Th14
                      .= (homography(N1)).(P) by Th17;
  end;
