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