Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Apply encode_u_ext with
x0,
λ x2 . ap (lam x0 (λ x3 . x1 x3)) x2,
λ x2 . x1 x2.
Let x2 of type ι be given.
Assume H0: x2 ∈ x0.
Apply beta with
x0,
x1,
x2.
The subproof is completed by applying H0.