Let x0 of type ι → (ι → (ι → ο) → ο) → (ι → ο) → ο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → (ι → ο) → ο . (∀ x4 . x4 ∈ x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply In_ind with
λ x1 . 2b1c2.. x0 x1 (In_rec_Vo2 x0 x1).
Let x1 of type ι be given.
Apply Descr_Vo2_prop with
2b1c2.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : (ι → ο) → ο . 2b1c2.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (In_rec_Vo2 x0).
Apply unknownprop_4827c395f66ed5e2b9711333b1b1681a1ac1c67519cd7de68052d7f43b6fa12f with
x0,
x1,
In_rec_Vo2 x0.
The subproof is completed by applying H1.
Apply unknownprop_57bc92e82cd111879864b413f133b93ca2216a7ee2b213ca5d0d3dcd74eef946 with
x0,
x1.
The subproof is completed by applying H0.