Let x0 of type ι → ((ι → ο) → ο) → ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Assume H0:
∀ x3 : (ι → ο) → ο . (∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ x5 ∈ x1) ⟶ iff (x2 x4) (x3 x4)) ⟶ x0 x1 x3 = x0 x1 x2.
Apply pack_c_0_eq2 with
x1,
x2,
λ x3 x4 . x0 x3 (decode_c (ap (pack_c x1 x2) 1)) = x0 x1 x2.
Apply H0 with
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.