reserve x,y for set,
  k,n for Nat,
  i for Integer,
  G for Group,
  a,b,c ,d,e for Element of G,
  A,B,C,D for Subset of G,
  H,H1,H2,H3,H4 for Subgroup of G ,
  N1,N2 for normal Subgroup of G,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem
  for N being normal Subgroup of G holds H * N = N * H
proof
  let N be normal Subgroup of G;
  thus H * N = carr H * N .= N * carr H by GROUP_3:120
    .= N * H;
end;
