theorem Th27:
  [.a",b.] = [.b,a.] |^ a"
proof
  thus [.a",b.] = a"" * (b" * (a" * b)) by Th16
    .= a"" * (b" * (a" * b)) * 1_G by GROUP_1:def 4
    .= a"" * (b" * (a" * b)) * (a * a") by GROUP_1:def 5
    .= a"" * (b" * (a" * b)) * a * a" by GROUP_1:def 3
    .= a"" * ((b" * (a" * b)) * a) * a" by GROUP_1:def 3
    .= [.b,a.] |^ a" by Th16;
end;
