Let x0 of type (ι → ι → ο) → ι → ι → ι → ι → ι → ι → ι → ι → ι → ο be given.
Assume H0:
∀ x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3) ⟶ 4402e.. x1 x2 ⟶ cf2df.. x1 x2 ⟶ ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ⊆ setminus x1 (Sing x3) ⟶ ∀ x5 . x5 ∈ x4 ⟶ ∀ x6 . x6 ∈ x4 ⟶ ∀ x7 . x7 ∈ x4 ⟶ ∀ x8 . x8 ∈ x4 ⟶ ∀ x9 . x9 ∈ x4 ⟶ ∀ x10 . x10 ∈ x4 ⟶ ∀ x11 . x11 ∈ x4 ⟶ ∀ x12 . x12 ∈ x4 ⟶ ∀ x13 . x13 ∈ x4 ⟶ x0 x2 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ 5bab1.. x1 x2.
Let x1 of type (ι → ι → ο) → ι → ι → ι → ι → ι → ι → ι → ι → ι → ο be given.
Assume H1:
∀ x2 . ∀ x3 : ι → ι → ο . (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ x3 x4 x5 ⟶ x3 x5 x4) ⟶ 4402e.. x2 x3 ⟶ cf2df.. x2 x3 ⟶ ∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ⊆ setminus x2 (Sing x4) ⟶ ∀ x6 . x6 ∈ x5 ⟶ ∀ x7 . x7 ∈ x5 ⟶ ∀ x8 . x8 ∈ x5 ⟶ ∀ x9 . x9 ∈ x5 ⟶ ∀ x10 . x10 ∈ x5 ⟶ ∀ x11 . x11 ∈ x5 ⟶ ∀ x12 . x12 ∈ x5 ⟶ ∀ x13 . x13 ∈ x5 ⟶ ∀ x14 . x14 ∈ x5 ⟶ x1 x3 x6 x7 x8 x9 x10 x11 x12 x13 x14 ⟶ 5bab1.. x2 x3.
Let x2 of type (ι → ι → ο) → ι → ι → ι → ι → ι → ι → ι → ι → ι → ο be given.
Assume H2:
∀ x3 . ∀ x4 : ι → ι → ο . (∀ x5 . x5 ∈ x3 ⟶ ∀ x6 . x6 ∈ x3 ⟶ x4 x5 x6 ⟶ x4 x6 x5) ⟶ 4402e.. x3 x4 ⟶ cf2df.. x3 x4 ⟶ ∀ x5 . x5 ∈ x3 ⟶ ∀ x6 . x6 ⊆ setminus x3 (Sing x5) ⟶ ∀ x7 . x7 ∈ x6 ⟶ ∀ x8 . x8 ∈ x6 ⟶ ∀ x9 . x9 ∈ x6 ⟶ ∀ x10 . x10 ∈ x6 ⟶ ∀ x11 . x11 ∈ x6 ⟶ ∀ x12 . x12 ∈ x6 ⟶ ∀ x13 . x13 ∈ x6 ⟶ ∀ x14 . x14 ∈ x6 ⟶ ∀ x15 . x15 ∈ x6 ⟶ x2 x4 x7 x8 x9 x10 x11 x12 x13 x14 x15 ⟶ 5bab1.. x3 x4.
Let x3 of type (ι → ι → ο) → ι → ι → ι → ι → ι → ι → ι → ι → ι → ο be given.
Assume H3:
∀ x4 . ∀ x5 : ι → ι → ο . ... ⟶ ... ⟶ ... ⟶ ∀ x6 . ... ⟶ ∀ x7 . ... ⟶ ∀ x8 . ... ⟶ ∀ x9 . ... ⟶ ∀ x10 . ... ⟶ ∀ x11 . ... ⟶ ∀ x12 . ... ⟶ ∀ x13 . ... ⟶ ∀ x14 . ... ⟶ ∀ x15 . ... ⟶ ∀ x16 . ... ⟶ x3 x5 x8 x9 x10 x11 x12 ... ... ... ... ⟶ 5bab1.. x4 x5.