Let x0 of type ι → (ι → ι) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Assume H0: ∀ x3 : ι → ι . (∀ x4 . x4 ∈ x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x3 = x0 x1 x2.
Apply pack_u_0_eq2 with
x1,
x2,
λ x3 x4 . x0 x3 (ap (ap (pack_u x1 x2) 1)) = x0 x1 x2.
Apply H0 with
ap (ap (pack_u x1 x2) 1).
Let x3 of type ι be given.
Assume H1: x3 ∈ x1.
Apply pack_u_1_eq2 with
x1,
x2,
x3.
The subproof is completed by applying H1.