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
  A <> {} & (for g1,g2 st g1 in A & g2 in A holds g1 * g2 in A) & (for
  g1 st g1 in A holds g1" in A) & (for o,g1 st g1 in A holds (G^o).g1 in A)
implies ex H being strict StableSubgroup of G st the carrier of H = A by Lm14;
