reserve x,O for set,
  o for Element of O,
  G,H,I for GroupWithOperators of O,
  A, B for Subset of G,
  N for normal StableSubgroup of G,
  H1,H2,H3 for StableSubgroup of G,
  g1,g2 for Element of G,
  h1,h2 for Element of H1,
  h for Homomorphism of G,H;

theorem Th56:
  for G being strict GroupWithOperators of O holds G,G./.(1).G are_isomorphic
proof
  let G be strict GroupWithOperators of O;
  nat_hom (1).G is bijective by Th54;
  hence thesis;
end;
