Let x0 of type ι be given.
Let x1 of type (ι → ο) → ο be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ο be given.
Let x6 of type ι → ο be given.
Let x7 of type ι be given.
Assume H0:
∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ x9 ∈ x0) ⟶ iff (x1 x8) (x2 x8).
Assume H1: ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x3 x8 x9 = x4 x8 x9.
Assume H2:
∀ x8 . x8 ∈ x0 ⟶ iff (x5 x8) (x6 x8).