Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_f8cb4609f9c174a593de5a10197e2915f5c1a2d9f32ed8d30c3d30b788bb9e1e with
λ x3 x4 : ι → ι → ι . In x2 (x4 x0 x1) ⟶ lam 2 (λ x5 . If_i (x5 = 0) (ap x2 0) (ap x2 1)) = x2.
The subproof is completed by applying unknownprop_8ae1b9c88f6fd7ee43f58cd7e8d5da6953e172beaf17889a2ce8ebd9d1a5b320 with x0, λ x3 . x1, x2.