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

theorem Th41:
  for G being Group
  for H being Subgroup of G
  for N being normal Subgroup of G
  st N is Subgroup of H
  holds the multMagma of N = the multMagma of (H,N)`*`
proof
  let G be Group;
  let H be Subgroup of G;
  let N be normal Subgroup of G;
  assume N is Subgroup of H;
  then N is normal Subgroup of H by GROUP_6:8;
  then reconsider N1=the multMagma of N as strict normal Subgroup of H
  by Th2;
  thus the multMagma of N = the multMagma of N1
                         .= the multMagma of (H,N)`*` by GROUP_6:def 1;
end;
