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 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x8 x9 = x6 x10 x11 ⟶ and (x8 = x10) (x9 = x11).
Assume H2:
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 x8 x9 = x3 x9 x8.
Assume H4:
∀ x8 . prim1 x8 x0 ⟶ x3 x1 x8 = x8.
Assume H6:
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x4 x9 x8.
Assume H8:
∀ x8 . prim1 x8 x0 ⟶ x4 x2 x8 = x8.
Assume H11:
∀ x8 . prim1 x8 x7 ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x8 = x6 x10 x11 ⟶ x9 (x6 x10 x11)) ⟶ x9 x8.
Assume H12:
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ (λ x10 . prim0 (λ x11 . and (prim1 x11 x0) (∃ x12 . and (prim1 x12 x0) (x10 = x6 x11 x12)))) (x6 x8 x9) = x8.
Assume H13:
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ (λ x10 . prim0 (λ x11 . and (prim1 x11 x0) (x10 = x6 ((λ x12 . prim0 (λ x13 . and (prim1 x13 x0) (∃ x14 . and (prim1 x14 x0) (x12 = x6 x13 x14)))) x10) x11))) (x6 x8 x9) = x9.
Assume H14:
∀ x8 . ... ⟶ prim1 (x6 x8 x1) (1216a.. x7 (λ x9 . (λ x10 . x6 ((λ x11 . prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 ... ...) ...))) ...) ...) ... = ...)).