theorem
  for O,N being Matrix of 3,REAL holds
  (N@ * O)@ * O * (N@ * O) = O@ * (N * O * N@) * O
  proof
    let O,N be Matrix of 3,REAL;
    (N@ * O)@ * O * (N@ * O) = (O@ * N@@) * O * (N@ * O) by MATRIXR2:30
                            .= (O@ * N) * O * (N@ * O) by MATRIXR2:29
                            .= (O@ * (N * O)) * (N@ * O) by MATRIXR2:27
                            .= (O@ * ((N * O) * (N@ * O))) by MATRIXR2:27
                            .= O@ * (((N * O) * N@) * O) by MATRIXR2:27;
    hence thesis by MATRIXR2:27;
  end;
