Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_c_b (ap x1 0) (decode_c (ap x1 1)) (decode_b (ap x1 2)).
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ι → ι be given.
Assume H1: ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ x3 x4 x5 ∈ x1.
Apply pack_c_b_0_eq2 with
x1,
x2,
x3,
λ x4 x5 . pack_c_b x1 x2 x3 = pack_c_b x4 (decode_c (ap (pack_c_b x1 x2 x3) 1)) (decode_b (ap (pack_c_b x1 x2 x3) 2)).
Apply pack_c_b_ext with
x1,
x2,
decode_c (ap (pack_c_b x1 x2 x3) 1),
x3,
decode_b (ap (pack_c_b x1 x2 x3) 2) leaving 2 subgoals.
Let x4 of type ι → ο be given.
Assume H2: ∀ x5 . x4 x5 ⟶ x5 ∈ x1.
Apply pack_c_b_1_eq2 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x4.
The subproof is completed by applying pack_c_b_2_eq2 with x1, x2, x3.