Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι → ι → ι be given.
Let x7 of type ι be given.
Assume H0:
∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x6 x8 x9 = x6 x10 x11 ⟶ and (x8 = x10) (x9 = x11).
Assume H2: ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x3 x8 x9 = x3 x9 x8.
Assume H3: x1 ∈ x0.
Assume H4: ∀ x8 . x8 ∈ x0 ⟶ x3 x1 x8 = x8.
Assume H5: ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x4 x8 x9 ∈ x0.
Assume H6:
∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ (λ x10 . prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x10 = x6 x11 x12)))) (x6 x8 x9) = x8.
Assume H7:
∀ x8 . x8 ∈ x0 ⟶ x6 x8 x1 ∈ {x9 ∈ x7|(λ x10 . x6 ((λ x11 . prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x11 = x6 x12 x13)))) x10) x1) x9 = x9}.
Assume H8:
∀ x8 . x8 ∈ x7 ⟶ (λ x9 . prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x9 = x6 x10 x11)))) x8 ∈ x0.
Assume H9:
∀ x8 . ... ⟶ ∀ x9 . ... ⟶ ∀ x10 . ... ⟶ ∀ x11 . ... ⟶ (λ x12 x13 . x6 (x3 ((λ x14 . prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x14 = x6 x15 x16)))) x12) ((λ x14 . prim0 (λ x15 . and (x15 ∈ x0) (∃ x16 . and (x16 ∈ x0) (x14 = x6 x15 x16)))) x13)) (x3 ((λ x14 . prim0 (λ x15 . and (x15 ∈ x0) (x14 = x6 ((λ x16 . prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x16 = x6 x17 x18)))) x14) x15))) x12) ((λ x14 . prim0 (λ x15 . and (x15 ∈ x0) (x14 = x6 ((λ x16 . prim0 (λ x17 . and (x17 ∈ x0) (∃ x18 . and (x18 ∈ x0) (x16 = x6 x17 x18)))) x14) x15))) ...))) ... ... = ....