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 Th19:
  for H being strict StableSubgroup of G holds H /\ H = H
proof
  let H be strict StableSubgroup of G;
  the carrier of H /\ H = carr(H) /\ carr(H) by Def25
    .= the carrier of H;
  hence thesis by Lm4;
end;
