 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);

theorem Th2: :: TH2
  for G being Group
  for N being normal Subgroup of G
  holds the multMagma of N is strict normal Subgroup of G
proof
  let G be Group;
  let N be normal Subgroup of G;
  reconsider N0 = the multMagma of N as strict Subgroup of G by Th1;

  for g being Element of G holds N0 |^ g = N0
  proof
    let g be Element of G;
    B2: N |^ g = the multMagma of N by GROUP_3:def 13;
    carr N = carr N0; then
    the carrier of (N0 |^ g) = (carr N) |^ g by GROUP_3:def 6
                            .= the carrier of N0 by B2, GROUP_3:def 6;
    hence N0 |^ g = N0 by GROUP_2:59;
  end;
  hence the multMagma of N is strict normal Subgroup of G
    by GROUP_3:def 13;
end;
