Let x0 of type ι → (ι → ι → ι → ο) → ι → ι → ο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → ι → ι → ο . (∀ x4 . x4 ∈ x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply In_ind with
λ x1 . 6b023.. x0 x1 (In_rec_iio x0 x1).
Let x1 of type ι be given.
Apply Descr_iio_prop with
6b023.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : ι → ι → ο . 6b023.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (In_rec_iio x0).
Apply unknownprop_29be8ffdeb96ec095470b8b15a1cf73c6a121f2e284a536ce1994939d01b3111 with
x0,
x1,
In_rec_iio x0.
The subproof is completed by applying H1.
Apply unknownprop_4eae4cdff7095dc248c158b66a75af5d5d5f509a99307d15479b03b8e365be22 with
x0,
x1.
The subproof is completed by applying H0.