 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 Ta1:
  for x,y,z being Element of EnsHomography3 holds
  (x (*) y) (*) z = x (*) (y (*) z)
  proof
    let x,y,z be Element of EnsHomography3;
    x in EnsHomography3;
    then consider Nx be invertible Matrix of 3,F_Real such that
A2: x = homography(Nx);
    y in EnsHomography3;
    then consider Ny be invertible Matrix of 3,F_Real such that
A3: y = homography(Ny);
    z in EnsHomography3;
    then consider Nz be invertible Matrix of 3,F_Real such that
A4: z = homography(Nz);
A5: width Nx = 3 & len Ny = 3 & width Ny = 3 & len Nz = 3 by MATRIX_0:24;
    y (*) z = homography(Ny * Nz) by A3,A4,Th18; then
A6: (x (*) (y (*) z)) = homography(Nx * (Ny * Nz)) by A2,Th18
    .= homography((Nx * Ny) * Nz) by A5,MATRIX_3:33;
    x (*) y = homography(Nx * Ny) by A2,A3,Th18;
    hence thesis by A6,A4,Th18;
  end;
