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.
Assume H9:
40e45.. x1 x2 x3 x4 x5 x6 x7 x8 x9.
Let x10 of type ο be given.
Assume H10:
28532.. x1 x2 x3 x4 x5 x6 x9 x8 ⟶ (x2 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x9 = x7 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x7 ⟶ ∀ x11 : ο . x11) ⟶ x1 x2 x7 ⟶ x1 x3 x7 ⟶ not (x1 x4 x7) ⟶ x1 x5 x7 ⟶ not (x1 x6 x7) ⟶ not (x1 x9 x7) ⟶ not (x1 x8 x7) ⟶ x10.
Apply H9 with
x10.
Assume H12:
28532.. x1 x2 x3 x4 x5 x6 x7 x8.
Apply H12 with
(x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x1 x2 x9 ⟶ x1 x3 x9 ⟶ not (x1 x4 x9) ⟶ x1 x5 x9 ⟶ not (x1 x6 x9) ⟶ not (x1 x7 x9) ⟶ not (x1 x8 x9) ⟶ x10.
Assume H13:
ba720.. x1 x2 x3 x4 x5 x6 x7.
Apply H13 with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x1 x2 x9 ⟶ x1 x3 x9 ⟶ not (x1 x4 x9) ⟶ x1 x5 x9 ⟶ not (x1 x6 x9) ⟶ not (x1 x7 x9) ⟶ not (x1 x8 x9) ⟶ x10.