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;
reserve E for set,
  A for Action of O,E,
  C for Subset of G,
  N1 for normal StableSubgroup of H1;

theorem Th87:
  for N1,N2 being strict StableSubgroup of G st N1 is normal
  StableSubgroup of H1 & N2 is normal StableSubgroup of H1 holds N1 "\/" N2 is
  normal StableSubgroup of H1
proof
  let N1,N2 be strict StableSubgroup of G;
  assume
A1: N1 is normal StableSubgroup of H1 & N2 is normal StableSubgroup of H1;
  then reconsider N19=N1,N29=N2 as StableSubgroup of H1;
  N1 "\/" N2 = N19 "\/" N29 by Th86;
  hence thesis by A1,Th32;
end;
