
theorem Th5:
  for X be RealNormSpace for f,g,h be Lipschitzian LinearOperator of X,X
  holds f*(g*h) =(f*g)*h
proof
  let X be RealNormSpace;
  let f,g,h be Lipschitzian LinearOperator of X,X;
  now
    let x be VECTOR of X;
    thus (f*(g*h)).x =f.((g*h).x) by Th4
      .= f.(g.(h.x)) by Th4
      .= (f*g).(h.x) by FUNCT_2:15
      .= ((f*g)*h).x by Th4;
  end;
  hence thesis by FUNCT_2:63;
end;
