Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_u_e (ap x1 0) (ap (ap x1 1)) (ap x1 2).
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Assume H1: ∀ x3 . x3 ∈ x1 ⟶ x2 x3 ∈ x1.
Let x3 of type ι be given.
Assume H2: x3 ∈ x1.
Apply pack_u_e_0_eq2 with
x1,
x2,
x3,
λ x4 x5 . pack_u_e x1 x2 x3 = pack_u_e x4 (ap (ap (pack_u_e x1 x2 x3) 1)) (ap (pack_u_e x1 x2 x3) 2).
Apply pack_u_e_2_eq2 with
x1,
x2,
x3,
λ x4 x5 . pack_u_e x1 x2 x3 = pack_u_e x1 (ap (ap (pack_u_e x1 x2 x3) 1)) x4.
Apply pack_u_e_ext with
x1,
x2,
ap (ap (pack_u_e x1 x2 x3) 1),
x3.
The subproof is completed by applying pack_u_e_1_eq2 with x1, x2, x3.