Let x0 of type ι → (ι → ι → ι) → CT2 ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Assume H0: ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ x1 ⟶ ∀ x6 . x6 ∈ x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . x6 ∈ x1 ⟶ ∀ x7 . x7 ∈ x1 ⟶ x3 x6 x7 = x5 x6 x7) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3.
Apply pack_b_b_0_eq2 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (decode_b (ap (pack_b_b x1 x2 x3) 1)) (decode_b (ap (pack_b_b x1 x2 x3) 2)) = x0 x1 x2 x3.
Apply H0 with
decode_b (ap (pack_b_b x1 x2 x3) 1),
decode_b (ap (pack_b_b x1 x2 x3) 2) leaving 2 subgoals.
The subproof is completed by applying pack_b_b_1_eq2 with x1, x2, x3.
The subproof is completed by applying pack_b_b_2_eq2 with x1, x2, x3.