Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ι → ι → ι be given.
Let x6 of type ι → ι → ι → ι be given.
Let x7 of type ι → ι → ι be given.
Let x8 of type ι → ι → ι → ι be given.
Let x9 of type ι → ι → ι → ι be given.
Let x10 of type ι → ι → ι be given.
Let x11 of type ι → ι → ι be given.
Let x12 of type ι → ι → ι be given.
Let x13 of type ι → ι → ι be given.
Apply unknownprop_f6577ef744ee240caee5f590e15fd6ef05a65801da70dc623c99d9fa33ed40ec with
λ x14 x15 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → ι → (ι → ι → ι) → (ι → ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι → ι) → (ι → ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → ο . x15 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ ∀ x16 : ο . (Loop x0 x1 x2 x3 x4 ⟶ (∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x5 x17 x18 = x2 (x1 x18 x17) (x1 x17 x18)) ⟶ (∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x6 x17 x18 x19 = x2 (x1 x17 (x1 x18 x19)) (x1 (x1 x17 x18) x19)) ⟶ (∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ and (and (and (and (x7 x17 x18 = x2 x17 (x1 x18 x17)) (x10 x17 x18 = x1 x17 (x1 x18 (x2 x17 x4)))) (x11 x17 x18 = x1 (x1 (x3 x4 x17) x18) x17)) (x12 x17 x18 = x1 (x2 x17 x18) (x2 (x2 x17 x4) x4))) (x13 x17 x18 = x1 (x3 x4 (x3 x4 x17)) (x3 x18 x17))) ⟶ (∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ and (x8 x17 x18 x19 = x2 (x1 x18 x17) (x1 x18 (x1 x17 x19))) (x9 x17 x18 x19 = x3 (x1 (x1 x19 x17) x18) (x1 x17 x18))) ⟶ x16) ⟶ x16.
The subproof is completed by applying unknownprop_bcfb235173b6e24d61b0900ebc9059688ec23fd5128404d7a36e3b666224a280 with
Loop x0 x1 x2 x3 x4,
∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x5 x14 x15 = x2 (x1 x15 x14) (x1 x14 x15),
∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x6 x14 x15 x16 = x2 (x1 x14 (x1 x15 x16)) (x1 (x1 x14 x15) x16),
∀ x14 . ... ⟶ ∀ x15 . ... ⟶ and (and (and (and (x7 x14 x15 = x2 x14 (x1 x15 x14)) (x10 ... ... = ...)) ...) ...) ...,
....