Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_c (ap x1 0) (decode_c (ap x1 1)).
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Apply pack_c_0_eq2 with
x1,
x2,
λ x3 x4 . pack_c x1 x2 = pack_c x3 (decode_c (ap (pack_c x1 x2) 1)).
Apply pack_c_ext with
x1,
x2,
decode_c (ap (pack_c x1 x2) 1).
Let x3 of type ι → ο be given.
Assume H1: ∀ x4 . x3 x4 ⟶ x4 ∈ x1.
Apply pack_c_1_eq2 with
x1,
x2,
x3,
λ x4 x5 : ο . iff (x2 x3) x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x3.