theorem Th2:
  for T being TopGroup, t being Point of T, f being Loop of t holds
  inverse_loop(f).x = (f.x)"
  proof
    let T be TopGroup;
    let t be Point of T;
    let f be Loop of t;
    thus inverse_loop(f).x = inverse_op(T).(f.x) by FUNCT_2:15
    .= (f.x)" by GROUP_1:def 6;
  end;
