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