Let x0 of type ι → (ι → ι → ο) → ι → ο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : 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_4a87b3b2bcf10bd0616cd3b0459f4ca1014c4bcd0183902ba6aaa9f0fef066b0 with
x0,
x1,
In_rec_Vo1 x0 x1,
x0 x1 (In_rec_Vo1 x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_90514bebae2be376719d62ecd84338b37c0dce3bc117145f4ba9847aabbcea9a with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_2de7add04e9052570d003c7f0d81aacd226a4576fd14fb0846deaf2686db7396 with
x0,
x1.
The subproof is completed by applying H0.