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.
Assume H7:
02ade.. x1 x2 x3 x4 x5 x6 x7.
Let x8 of type ο be given.
Assume H8:
c5756.. x1 x5 x4 x3 x2 x7 ⟶ (x5 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x7 = x6 ⟶ ∀ x9 : ο . x9) ⟶ x1 x5 x6 ⟶ x1 x4 x6 ⟶ not (x1 x3 x6) ⟶ not (x1 x2 x6) ⟶ x1 x7 x6 ⟶ x8.
Apply H7 with
x8.
Assume H10:
c5756.. x1 x2 x3 x4 x5 x6.
Apply H10 with
(x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x1 x2 x7 ⟶ x1 x3 x7 ⟶ not (x1 x4 x7) ⟶ not (x1 x5 x7) ⟶ x1 x6 x7 ⟶ x8.
Assume H11:
8b6ad.. x1 x2 x3 x4 x5.
Apply H11 with
(x2 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x6 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x6 ⟶ ∀ x9 : ο . x9) ⟶ not (x1 x2 x6) ⟶ not (x1 x3 x6) ⟶ x1 x4 x6 ⟶ x1 x5 x6 ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x1 x2 x7 ⟶ x1 x3 x7 ⟶ not (x1 x4 x7) ⟶ not (x1 x5 x7) ⟶ x1 x6 x7 ⟶ x8.
Assume H12: x2 = x3 ⟶ ∀ x9 : ο . x9.
Assume H13: x2 = x4 ⟶ ∀ x9 : ο . x9.
Assume H14: x3 = x4 ⟶ ∀ x9 : ο . x9.
Assume H15: x2 = x5 ⟶ ∀ x9 : ο . x9.
Assume H16: x3 = x5 ⟶ ∀ x9 : ο . x9.
Assume H17: x4 = x5 ⟶ ∀ x9 : ο . x9.