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.
Let x1 of type ι be given.
Apply unknownprop_4eae4cdff7095dc248c158b66a75af5d5d5f509a99307d15479b03b8e365be22 with
x0,
x1,
In_rec_iio x0 x1,
x0 x1 (In_rec_iio x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_4a2f5327815bc8d6b514b716d12bbe30a84529c2301139001d9de9a305fdaf30 with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_0972079d65757b8b7dea4e78f0f4f964fc8351ee591584a33a89198d1c4fe74e with
x0,
x1.
The subproof is completed by applying H0.