Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ο be given.
Let x4 of type ι → ο be given.
Assume H1:
∀ x5 . ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x5 ⟶ ∀ x8 . prim1 x8 x5 ⟶ prim1 (x6 x7 x8) x5) ⟶ ∀ x7 : ι → ι → ο . ∀ x8 : ι → ο . x4 (0fd05.. x5 x6 x7 x8).
Apply H1 with
x0,
x1,
x2,
x3.
The subproof is completed by applying H0.