theorem Th38:
  a in H & b in H implies [.a,b.] in H
proof
  assume
A1: a in H & b in H;
  then a" in H & b" in H by GROUP_2:51;
  then
A2: a" * b" in H by GROUP_2:50;
  a * b in H by A1,GROUP_2:50;
  then (a" * b") * (a * b) in H by A2,GROUP_2:50;
  hence thesis by Th16;
end;
