Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_e_e (ap x1 0) (ap x1 1) (ap x1 2).
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H1: x2 ∈ x1.
Let x3 of type ι be given.
Assume H2: x3 ∈ x1.
Apply pack_e_e_0_eq2 with
x1,
x2,
x3,
λ x4 x5 . pack_e_e x1 x2 x3 = pack_e_e x4 (ap (pack_e_e x1 x2 x3) 1) (ap (pack_e_e x1 x2 x3) 2).
Apply pack_e_e_1_eq2 with
x1,
x2,
x3,
λ x4 x5 . pack_e_e x1 x2 x3 = pack_e_e x1 x4 (ap (pack_e_e x1 x2 x3) 2).
Apply pack_e_e_2_eq2 with
x1,
x2,
x3,
λ x4 x5 . pack_e_e x1 x2 x3 = pack_e_e x1 x2 x4.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H3.