Let x0 of type ι → (ι → ι → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Assume H0:
∀ x3 : ι → ι → ο . (∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ iff (x2 x4 x5) (x3 x4 x5)) ⟶ x0 x1 x3 = x0 x1 x2.
Apply pack_r_0_eq2 with
x1,
x2,
λ x3 x4 . x0 x3 (decode_r (ap (pack_r x1 x2) 1)) = x0 x1 x2.
Apply H0 with
decode_r (ap (pack_r x1 x2) 1).
Let x3 of type ι be given.
Assume H1: x3 ∈ x1.
Let x4 of type ι be given.
Assume H2: x4 ∈ x1.
Apply pack_r_1_eq2 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x3 x4) x5 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x3 x4.