Let x0 of type ι → (ι → (ι → ο) → ο) → (ι → ο) → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → (ι → ο) → ο . (∀ x4 . prim1 x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Let x1 of type ι be given.
Apply unknownprop_57bc92e82cd111879864b413f133b93ca2216a7ee2b213ca5d0d3dcd74eef946 with
x0,
x1,
In_rec_Vo2 x0 x1,
x0 x1 (In_rec_Vo2 x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_a8c97ae0a017afe69d44636ace2d181933ab2539bdda35cb9471bd768df945ae with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_dae3b4285212b91c2ce9da68d8544d08d0c7b1be3e30666e0091105c9f3f910e with
x0,
x1.
The subproof is completed by applying H0.