theorem Th56:
  H1 is Subgroup of H2 & H3 is Subgroup of H4 implies commutators(
  H1,H3) c= commutators(H2,H4)
proof
  assume H1 is Subgroup of H2 & H3 is Subgroup of H4;
  then the carrier of H1 c= the carrier of H2 & the carrier of H3 c= the
  carrier of H4 by GROUP_2:def 5;
  hence thesis by Th50;
end;
