Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_b (ap x1 0) (decode_b (ap x1 1)).
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Assume H1: ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ∈ x1.
Apply pack_b_0_eq2 with
x1,
x2,
λ x3 x4 . pack_b x1 x2 = pack_b x3 (decode_b (ap (pack_b x1 x2) 1)).
Apply pack_b_ext with
x1,
x2,
decode_b (ap (pack_b x1 x2) 1).
The subproof is completed by applying pack_b_1_eq2 with x1, x2.