Proof.We just show the proof for the rst form. Because , 9m; n 2
L(X) s:t: m = ; n = .Assuming x 2 X which means x = 0,
then(x m) ( m) = = 0 which means x m 2 X. And as
m 2 L(X), x 6= y ) x m 6= y m. So, () (). In the same argument,
() (). As a result, () = () which means
:=
.
And what's more.