
theorem
  for X being non empty set, T being associative non empty multMagma
  for f,g,h being Function of X,T holds f(#)g(#)h = f(#)(g(#)h)
  proof
    let X be non empty set;
    let T be associative non empty multMagma;
    let f,g,h be Function of X,T;
    let x be Element of X;
    thus (f(#)g(#)h).x = (f(#)g).x*h.x by Def2
    .= f.x*g.x*h.x by Def2
    .= f.x*(g.x*h.x) by GROUP_1:def 3
    .= f.x*(g(#)h).x by Def2
    .= (f(#)(g(#)h)).x by Def2;
  end;
