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.

Assume H1: 4402e.. x0 x1.

Assume H2: cf2df.. x0 x1.

Let x2 of type ι be given.

Assume H3: x2 ∈ x0.

Let x3 of type ι be given.

Assume H4: x3 ⊆ setminus x0 (Sing x2).

Claim L5: ...

...

Let x4 of type ι be given.

Assume H6: x4 ∈ x3.

Let x5 of type ι be given.

Assume H7: x5 ∈ x3.

Let x6 of type ι be given.

Assume H8: x6 ∈ x3.

Let x7 of type ι be given.

Assume H9: x7 ∈ x3.

Let x8 of type ι be given.

Assume H10: x8 ∈ x3.

Let x9 of type ι be given.

Assume H11: x9 ∈ x3.

Let x10 of type ι be given.

Assume H12: x10 ∈ x3.

Let x11 of type ι be given.

Assume H13: x11 ∈ x3.

Let x12 of type ι be given.

Assume H14: x12 ∈ x3.

Let x13 of type ι be given.

Assume H15: x13 ∈ x3.

Let x14 of type ι be given.

Assume H16: x14 ∈ x3.

Assume H17: d09d5.. x1 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14.

Let x15 of type ο be given.

Assume H18: ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ d1f25.. x1 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 ⟶ x15.

Assume H19: ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ 9f2b5.. x1 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 ⟶ x15.

Assume H20: ∀ x16 . ... ⟶ ∀ x17 . ... ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ ∀ x25 . x25 ∈ x0 ⟶ ∀ x26 . x26 ∈ x0 ⟶ ∀ x27 . x27 ∈ x0 ⟶ f55c6.. x1 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 ⟶ x15.

...

■

Proofgold Proof