Let x0 of type ι → (ι → (((ι → ο) → ο) → ο) → ο) → (((ι → ο) → ο) → ο) → ο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → (((ι → ο) → ο) → ο) → ο . (∀ x4 . x4 ∈ x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply In_ind with
λ x1 . 461b4.. x0 x1 (In_rec_Vo4 x0 x1).
Let x1 of type ι be given.
Apply Descr_Vo4_prop with
461b4.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : (((ι → ο) → ο) → ο) → ο . 461b4.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (In_rec_Vo4 x0).
Apply unknownprop_baa64b0dc3150faa2aa910b1d0b43f6e89eea54fa7fdbb099eecf828a22d69a1 with
x0,
x1,
In_rec_Vo4 x0.
The subproof is completed by applying H1.
Apply unknownprop_30ddc768878844a84528ac4e845a2f81437458ecc81ad73fcb6b32ab7dec1955 with
x0,
x1.
The subproof is completed by applying H0.