On slide 13, we defined β as (b => true | (a => true | false)), and numbered it as N_22 (where (a => true | false) was called N_2, true was N_1, false was N_0).

The root node of N_13 and N_22 is in both cases b. Hence, we add the b node, and propagate the apply-call both on the high- and and the low-edges. We get:

(b ? Apply(→, N_2,N_1) : Apply(→, N_1,N_2))

Node N_1 is the 1-node. This turns Apply(→, N_2,N_1) to N_1 (as anything→true is always true), and it turns Apply(→, N_1,N_2) to N_2 (as true→X always depends precisely on X). Now, we have:

(b ? true : N_2) or (b ? N_1 : N_2) (as we called the true-leaf N_1)

But this exactly what we defined N_22 (the BDD of β) to be. Thus, our result is equal to N_22.