theorem Th18:
  (for H being StableSubgroup of G st H = H1 /\ H2 holds the
carrier of H = (the carrier of H1) /\ (the carrier of H2)) & for H being strict
  StableSubgroup of G holds the carrier of H = (the carrier of H1) /\ (the
  carrier of H2) implies H = H1 /\ H2
proof
A1: the carrier of H1 = carr(H1) & the carrier of H2 = carr(H2);
  thus for H being StableSubgroup of G st H = H1 /\ H2 holds the carrier of H
  = (the carrier of H1) /\ (the carrier of H2)
  proof
    let H be StableSubgroup of G;
    assume H = H1 /\ H2;
    hence the carrier of H = carr(H1)/\carr(H2) by Def25
      .= (the carrier of H1)/\(the carrier of H2);
  end;
  let H be strict StableSubgroup of G;
  assume the carrier of H = (the carrier of H1) /\ (the carrier of H2);
  hence thesis by A1,Def25;
end;
