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 Th38:
  for H2,H3 being strict StableSubgroup of G holds H1 is
  StableSubgroup of H2 implies H1 "\/" H3 is StableSubgroup of H2 "\/" H3
proof
  let H2,H3 be strict StableSubgroup of G;
  assume H1 is StableSubgroup of H2;
  then H1 is Subgroup of H2 by Def7;
  then carr H1 c= carr H2 by GROUP_2:def 5;
  hence thesis by Th26,XBOOLE_1:9;
end;
