Lemma 2.1.4. Assuming that:

$M$ and $N$ are $λ$ -terms

Then

(1)
$FV (M^{*}) \subseteq FV (M)$ ;
(2)
$M ↠_{β} M^{*}$ ;
(3)
If $M \to_{β} N$ , then $N ↠_{β} M^{*}$ .