theorem Th16:
  [.a,b.] = a" * b" * a * b & [.a,b.] = a" * (b" * a) * b & [.a,b
.] = a" * (b" * a * b) & [.a,b.] = a" * (b" * (a * b)) & [.a,b.] = (a" * b") *
  (a * b)
proof
  thus [.a,b.] = a" * b" * a * b;
  thus [.a,b.] = a" * (b" * a) * b by GROUP_1:def 3;
  hence [.a,b.] = a" * (b" * a * b) by GROUP_1:def 3;
  hence [.a,b.] = a" * (b" * (a * b)) by GROUP_1:def 3;
  thus thesis by GROUP_1:def 3;
end;
