Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_e (ap x1 0) (ap x1 1).
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H1: x2 ∈ x1.
Apply pack_e_0_eq2 with
x1,
x2,
λ x3 x4 . pack_e x1 x2 = pack_e x3 (ap (pack_e x1 x2) 1).
Apply pack_e_1_eq2 with
x1,
x2,
λ x3 x4 . pack_e x1 x2 = pack_e x1 x3.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H2.