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.
Let x12 of type ι be given.
Assume H11: x12 ∈ x0.
Assume H12:
ce66c.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12.
Let x13 of type ο be given.
Assume H13:
94275.. x1 x7 x9 x6 x8 x4 x2 x5 x3 x11 x10 ⟶ (x7 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x9 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x2 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x11 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x10 = x12 ⟶ ∀ x14 : ο . x14) ⟶ not (x1 x7 x12) ⟶ x1 x9 x12 ⟶ not (x1 x6 x12) ⟶ not (x1 x8 x12) ⟶ not (x1 x4 x12) ⟶ not (x1 x2 x12) ⟶ not (x1 x5 x12) ⟶ x1 x3 x12 ⟶ not (x1 x11 x12) ⟶ not (x1 x10 x12) ⟶ x13.
Apply H12 with
x13.
Assume H14:
94275.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11.
Assume H15: x2 = x12 ⟶ ∀ x14 : ο . x14.
Assume H16: x3 = x12 ⟶ ∀ x14 : ο . x14.
Assume H17: x4 = x12 ⟶ ∀ x14 : ο . x14.
Assume H18: x5 = x12 ⟶ ∀ x14 : ο . x14.
Assume H19: x6 = x12 ⟶ ∀ x14 : ο . x14.
Assume H20: x7 = x12 ⟶ ∀ x14 : ο . x14.
Assume H21: x8 = x12 ⟶ ∀ x14 : ο . x14.
Assume H22: x9 = x12 ⟶ ∀ x14 : ο . x14.
Assume H23: x10 = x12 ⟶ ∀ x14 : ο . x14.
Assume H24: x11 = x12 ⟶ ∀ x14 : ο . x14.
Assume H25:
not (x1 x2 x12).
Assume H26: x1 x3 x12.
Assume H27:
not (x1 x4 x12).
Assume H28:
not (x1 x5 x12).
Assume H29:
not (x1 x6 x12).