theorem Th25:
  for H being strict StableSubgroup of G holds
  the_stable_subgroup_of carr H = H
proof
  let H be strict StableSubgroup of G;
  for H1 be strict StableSubgroup of G st carr H c= the carrier of H1
  holds H is StableSubgroup of H1 by Lm20;
  hence thesis by Def26;
end;
