
theorem
  for I be non empty set,
      G be Group,
      F be internal DirectSumComponents of G,I
  holds F is Subgroup-Family of I,G
  proof
    let I be non empty set,
        G be Group,
        F be internal DirectSumComponents of G,I;
    for i be object st i in I holds F.i is Subgroup of G by GROUP_19:def 9;
    hence thesis by GROUP_20:def 1;
  end;
