Let x0 of type ι → ι → ι → ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply pack_e_e_0_eq2 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (ap (pack_e_e x1 x2 x3) 1) (ap (pack_e_e x1 x2 x3) 2) = x0 x1 x2 x3.
Apply pack_e_e_1_eq2 with
x1,
x2,
x3,
λ x4 x5 . x0 x1 x4 (ap (pack_e_e x1 x2 x3) 2) = x0 x1 x2 x3.
Apply pack_e_e_2_eq2 with
x1,
x2,
x3,
λ x4 x5 . x0 x1 x2 x4 = x0 x1 x2 x3.
Let x4 of type ο → ο → ο be given.
Assume H0: x4 (x0 x1 x2 x3) (x0 x1 x2 x3).
The subproof is completed by applying H0.