theorem
  H1 is Subgroup of H2 & H3 is Subgroup of H4 implies [.H1,H3.] is
  Subgroup of [.H2,H4.]
proof
  assume H1 is Subgroup of H2 & H3 is Subgroup of H4;
  then commutators(H1,H3) c= commutators(H2,H4) by Th56;
  hence thesis by GROUP_4:32;
end;
