Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0:
x0 = lam 2 (λ x3 . If_i (x3 = 0) x1 x2).
Apply H0 with
λ x3 x4 . x2 = ap x4 1.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying tuple_2_1_eq with x1, x2, λ x4 x5 . x3 x5 x4.