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