theorem Th22:
  [.a,b.]" = [.b,a.]
proof
  thus [.a,b.]" = ((a" * b") * (a * b))" by Th16
    .= (a * b)" * (a" * b")" by GROUP_1:17
    .= (b" * a") * (a" * b")" by GROUP_1:17
    .= (b" * a") * (b"" * a"") by GROUP_1:17
    .= (b" * a") * (b"" * a)
    .= (b" * a") * (b * a)
    .= [.b,a.] by Th16;
end;
