Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Assume H0: ∀ x9 . x9 ∈ x8 ⟶ ∀ x10 : ι → ο . x10 x0 ⟶ x10 x1 ⟶ x10 x2 ⟶ x10 x3 ⟶ x10 x4 ⟶ x10 x5 ⟶ x10 x6 ⟶ x10 x7 ⟶ x10 x9.
Let x9 of type ι be given.
Assume H1: x9 ⊆ x8.
Let x10 of type ο be given.
Assume H3: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x2 ∈ x9 ⟶ x3 ∈ x9 ⟶ x10.
Assume H4: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x2 ∈ x9 ⟶ x4 ∈ x9 ⟶ x10.
Assume H5: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x3 ∈ x9 ⟶ x4 ∈ x9 ⟶ x10.
Assume H6: x0 ∈ x9 ⟶ x2 ∈ x9 ⟶ x3 ∈ x9 ⟶ x4 ∈ x9 ⟶ x10.
Assume H7: x1 ∈ x9 ⟶ x2 ∈ x9 ⟶ x3 ∈ x9 ⟶ x4 ∈ x9 ⟶ x10.
Assume H8: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x2 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H9: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x3 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H10: x0 ∈ x9 ⟶ x2 ∈ x9 ⟶ x3 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H11: x1 ∈ x9 ⟶ x2 ∈ x9 ⟶ x3 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H12: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x4 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H13: x0 ∈ x9 ⟶ x2 ∈ x9 ⟶ x4 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H14: x1 ∈ x9 ⟶ x2 ∈ x9 ⟶ x4 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H15: x0 ∈ x9 ⟶ x3 ∈ x9 ⟶ x4 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H16: x1 ∈ x9 ⟶ x3 ∈ x9 ⟶ x4 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H17: x2 ∈ x9 ⟶ x3 ∈ x9 ⟶ x4 ∈ x9 ⟶ x5 ∈ x9 ⟶ x10.
Assume H18: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x2 ∈ x9 ⟶ x6 ∈ x9 ⟶ x10.
Assume H19: x0 ∈ x9 ⟶ x1 ∈ x9 ⟶ x3 ∈ x9 ⟶ x6 ∈ x9 ⟶ x10.
Assume H20: x0 ∈ x9 ⟶ x2 ∈ x9 ⟶ x3 ∈ x9 ⟶ x6 ∈ x9 ⟶ x10.
Assume H21: ... ⟶ x2 ∈ ... ⟶ x3 ∈ x9 ⟶ x6 ∈ x9 ⟶ x10.