theorem
  (s*')" = (s")*'
proof
  now
    let n be Element of NAT;
    thus (s*')".n = (s*'.n)" by VALUED_1:10
      .= ((s.n)*')" by Def2
      .= ((s.n)")*' by COMPLEX1:36
      .= (s".n)*' by VALUED_1:10
      .= (s")*'.n by Def2;
  end;
  hence thesis by FUNCT_2:63;
end;
