Let x0 of type ι → (ι → ι) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Apply unknownprop_7461507986cbf49e907e297fd5f04e13d3ceb8c3463464280e794a94eb50b6a5 with
λ x3 x4 : (ι → (ι → ι) → ι) → ι → ι → ο . (∀ x5 . In x5 x1 ⟶ x4 x0 x5 (x2 x5)) ⟶ x4 x0 x1 (x0 x1 x2).
Assume H0:
∀ x3 . In x3 x1 ⟶ ∀ x4 : ι → ι → ο . (∀ x5 . ∀ x6 : ι → ι . (∀ x7 . In x7 x5 ⟶ x4 x7 (x6 x7)) ⟶ x4 x5 (x0 x5 x6)) ⟶ x4 x3 (x2 x3).
Let x3 of type ι → ι → ο be given.
Assume H1:
∀ x4 . ∀ x5 : ι → ι . (∀ x6 . In x6 x4 ⟶ x3 x6 (x5 x6)) ⟶ x3 x4 (x0 x4 x5).
Apply H1 with
x1,
x2.
Let x4 of type ι be given.
Apply H0 with
x4,
x3 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H1.