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 Th10:
  G is StableSubgroup of G
proof
A1: for o being Element of O holds G^o = (G^o)|the carrier of G;
  G is Subgroup of G by GROUP_2:54;
  hence thesis by A1,Def7;
end;
