Let x0 of type ι be given.
Let x1 of type (ι → ο) → ο be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι → ι → ο be given.
Let x5 of type ι → ο be given.
Assume H1:
∀ x6 . ∀ x7 : (ι → ο) → ο . ∀ x8 : ι → ι . (∀ x9 . prim1 x9 x6 ⟶ prim1 (x8 x9) x6) ⟶ ∀ x9 x10 : ι → ι → ο . x5 (34992.. x6 x7 x8 x9 x10).
Apply H1 with
x0,
x1,
x2,
x3,
x4.
The subproof is completed by applying H0.