Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.
Let x2 of type ι be given.
Assume H1: x2 ∈ x0.
Let x3 of type ι be given.
Assume H2: x3 ∈ x0.
Let x4 of type ι be given.
Assume H3: x4 ∈ x0.
Let x5 of type ι be given.
Assume H4: x5 ∈ x0.
Let x6 of type ι be given.
Assume H5: x6 ∈ x0.
Let x7 of type ι be given.
Assume H6: x7 ∈ x0.
Let x8 of type ι be given.
Assume H7: x8 ∈ x0.
Assume H8:
c8dd3.. x1 x2 x3 x4 x5 x6 x7 x8.
Let x9 of type ο be given.
Assume H9:
1e330.. x1 x2 x3 x4 x5 x6 x8 ⟶ (x2 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x8 = x7 ⟶ ∀ x10 : ο . x10) ⟶ x1 x2 x7 ⟶ x1 x3 x7 ⟶ x1 x4 x7 ⟶ x1 x5 x7 ⟶ not (x1 x6 x7) ⟶ not (x1 x8 x7) ⟶ x9.
Apply H8 with
x9.
Assume H11:
1e330.. x1 x2 x3 x4 x5 x6 x7.
Apply H11 with
(x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ x1 x2 x8 ⟶ x1 x3 x8 ⟶ x1 x4 x8 ⟶ x1 x5 x8 ⟶ not (x1 x6 x8) ⟶ not (x1 x7 x8) ⟶ x9.
Assume H12:
2b028.. x1 x2 x3 x4 x5 x6.
Apply H12 with
... ⟶ (... ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x7 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x7 ⟶ ∀ x10 : ο . x10) ⟶ x1 x2 x7 ⟶ x1 x3 x7 ⟶ x1 x4 x7 ⟶ x1 x5 x7 ⟶ not (x1 x6 x7) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ x1 x2 x8 ⟶ x1 x3 x8 ⟶ x1 x4 x8 ⟶ x1 x5 x8 ⟶ not (x1 x6 x8) ⟶ not (x1 x7 x8) ⟶ x9.