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 . Loop x0 x1 x2 x3 x4 ⟶ (∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x5 x16 x17 = x2 (x1 x17 x16) (x1 x16 x17)) ⟶ (∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x6 x16 x17 x18 = x2 (x1 x16 (x1 x17 x18)) (x1 (x1 x16 x17) x18)) ⟶ (∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ and (and (and (and (x7 x16 x17 = x2 x16 (x1 x17 x16)) (x10 x16 x17 = x1 x16 (x1 x17 (x2 x16 x4)))) (x11 x16 x17 = x1 (x1 (x3 x4 x16) x17) x16)) (x12 x16 x17 = x1 (x2 x16 x17) (x2 (x2 x16 x4) x4))) (x13 x16 x17 = x1 (x3 x4 (x3 x4 x16)) (x3 x17 x16))) ⟶ (∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ and (x8 x16 x17 x18 = x2 (x1 x17 x16) (x1 x17 (x1 x16 x18))) (x9 x16 x17 x18 = x3 (x1 (x1 x18 x16) x17) (x1 x16 x17))) ⟶ x15 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13.
The subproof is completed by applying unknownprop_9b09b99fce48fbc4294fba4077c15371ba18b57a0bc4e20cfa1cf1c48cd99108 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 x14 x15 = x1 ... ...)) ...) ...) ...,
....