Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Assume H0:
∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0.
Let x2 of type ι → ι → ι be given.
Assume H1:
∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ In (x2 x3 x4) x0.
Let x3 of type ι → ι → ι be given.
Assume H2:
∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 x0 ⟶ In (x3 x4 x5) x0.
Let x4 of type ι → ι → ι → ι be given.
Assume H3:
∀ x5 . In x5 x0 ⟶ ∀ x6 . In x6 x0 ⟶ ∀ x7 . In x7 x0 ⟶ In (x4 x5 x6 x7) x0.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι → ι → ι → ι be given.
Assume H6:
∀ x8 . In x8 x0 ⟶ ∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x7 x8 x9 x10) x0.
Let x8 of type ι → ι → ι be given.
Assume H7:
∀ x9 . In x9 x0 ⟶ ∀ x10 . In x10 x0 ⟶ In (x8 x9 x10) x0.
Let x9 of type ι → ι → ι be given.
Assume H8:
∀ x10 . In x10 x0 ⟶ ∀ x11 . In x11 x0 ⟶ In (x9 x10 x11) x0.
Let x10 of type ι be given.
Let x11 of type ι → ι → ι be given.
Assume H10:
∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ In (x11 x12 x13) x0.
Assume H11:
∀ x12 . In x12 x0 ⟶ (x11 x10 x12 = x12 ⟶ False) ⟶ False.
Assume H12:
∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x1 x12 (x11 x12 x13) = x13 ⟶ False) ⟶ False.
Assume H13:
∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x11 x12 (x1 x12 x13) = x13 ⟶ False) ⟶ False.
Assume H14:
∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x2 (x11 x13 x12) x12 = x13 ⟶ False) ⟶ False.
Assume H15:
∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ (x11 (x2 x13 x12) x12 = x13 ⟶ False) ⟶ False.
Assume H16:
∀ x12 . In x12 x0 ⟶ ∀ x13 . In x13 x0 ⟶ ∀ x14 . In x14 x0 ⟶ x11 x13 x12 = x11 x14 x12 ⟶ (x13 = x14 ⟶ False) ⟶ False.
Assume H17:
∀ x12 . ... ⟶ ∀ x13 . ... ⟶ (x9 x12 x13 = x11 (x1 x12 x13) (x1 (x1 ... ...) ...) ⟶ False) ⟶ False.