Proposition 2.1.14. Define the $λ$ -terms:

$⊤ : = λ x . λ y . x$
$⊥ : = λ x . λ y . y$
$(if B then P else Q : = B P Q)$

Then for $λ$ -terms $P$ and $Q$ , we have

(i)
$(if ⊤ then P else Q) \equiv_{β} P$ ;
(ii)
$(if ⊥ then P else Q) \equiv_{β} Q$ .