Let x0 of type ι → (ι → ((ι → ο) → ο) → ο) → ((ι → ο) → ο) → ο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → ((ι → ο) → ο) → ο . (∀ x4 . x4 ∈ x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply In_ind with
λ x1 . b9fc2.. x0 x1 (In_rec_Vo3 x0 x1).
Let x1 of type ι be given.
Apply Descr_Vo3_prop with
b9fc2.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : ((ι → ο) → ο) → ο . b9fc2.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (In_rec_Vo3 x0).
Apply unknownprop_19e14cfefa9c62802c3472f7b613074ec9e1720289fb25abc9d15e165cea68de with
x0,
x1,
In_rec_Vo3 x0.
The subproof is completed by applying H1.
Apply unknownprop_e3fd7e34e0da9eea44164f3141ff6fc232704ab917a0a07eb8451b62e6e7b7c2 with
x0,
x1.
The subproof is completed by applying H0.