Let x0 of type ι → (ι → (ι → ο) → ο) → (ι → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → (ι → ο) → ο be given.
Assume H0:
∀ x3 . In x3 x1 ⟶ 59843.. x0 x3 (x2 x3).
Let x3 of type ι → ((ι → ο) → ο) → ο be given.
Assume H1:
∀ x4 . ∀ x5 : ι → (ι → ο) → ο . (∀ 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.