theorem Th39:
  for X,Y being StableSubgroup of H1, X9,Y9 being StableSubgroup
  of G st X = X9 & Y = Y9 holds X9 /\ Y9 = X /\ Y
proof
  let X,Y be StableSubgroup of H1;
  reconsider Z = X /\ Y as StableSubgroup of G by Th11;
  let X9,Y9 be StableSubgroup of G;
  assume
A1: X=X9 & Y=Y9;
  the carrier of X /\ Y = (carr X) /\ (carr Y) by Def25;
  then X9 /\ Y9 = Z by A1,Th18;
  hence thesis;
end;
