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.
Let x9 of type ι be given.
Assume H8: x9 ∈ x0.
Let x10 of type ι be given.
Assume H9: x10 ∈ x0.
Let x11 of type ι be given.
Assume H10: x11 ∈ x0.
Assume H11:
60dbb.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11.
Let x12 of type ο be given.
Assume H12:
7db3a.. x1 x2 x10 x11 x5 x6 x7 x9 x8 x3 ⟶ (x2 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x11 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x4 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x4 ⟶ ∀ x13 : ο . x13) ⟶ not (x1 x2 x4) ⟶ x1 x10 x4 ⟶ not (x1 x11 x4) ⟶ not (x1 x5 x4) ⟶ x1 x6 x4 ⟶ not (x1 x7 x4) ⟶ not (x1 x9 x4) ⟶ x1 x8 x4 ⟶ not (x1 x3 x4) ⟶ x12.
Apply H11 with
x12.
Assume H14:
7db3a.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10.
Apply H14 with
(x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x1 x2 x11) ⟶ x1 x3 x11 ⟶ not (x1 x4 x11) ⟶ not (x1 x5 x11) ⟶ x1 x6 x11 ⟶ not (x1 x7 x11) ⟶ not (x1 x8 x11) ⟶ x1 x9 x11 ⟶ not (x1 x10 x11) ⟶ x12.
Assume H15:
c8b10.. x1 x2 x3 x4 x5 x6 x7 x8 x9.
Apply H15 with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ not (x1 x10 ...) ⟶ x12.