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:
df3c6.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12.
Let x13 of type ο be given.
Assume H13:
f1c88.. x1 x12 x11 x10 x5 x7 x6 x9 x8 x4 x3 ⟶ (x12 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x11 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x10 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x9 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x4 = x2 ⟶ ∀ x14 : ο . x14) ⟶ (x3 = x2 ⟶ ∀ x14 : ο . x14) ⟶ not (x1 x12 x2) ⟶ x1 x11 x2 ⟶ x1 x10 x2 ⟶ not (x1 x5 x2) ⟶ not (x1 x7 x2) ⟶ not (x1 x6 x2) ⟶ not (x1 x9 x2) ⟶ x1 x8 x2 ⟶ not (x1 x4 x2) ⟶ not (x1 x3 x2) ⟶ x13.
Apply H12 with
x13.
Assume H15:
f1c88.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11.
Apply H15 with
... ⟶ ... ⟶ (x4 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x5 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x6 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x7 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x8 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x9 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x10 = x12 ⟶ ∀ x14 : ο . x14) ⟶ (x11 = x12 ⟶ ∀ x14 : ο . x14) ⟶ not (x1 x2 x12) ⟶ x1 x3 x12 ⟶ x1 x4 x12 ⟶ not (x1 x5 x12) ⟶ not (x1 x6 x12) ⟶ not (x1 x7 x12) ⟶ not (x1 x8 x12) ⟶ x1 x9 x12 ⟶ not (x1 x10 x12) ⟶ not (x1 x11 x12) ⟶ x13.