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.
Assume H1:
∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 x7 (x3 x8 x9) = x3 (x3 x7 x8) x9.
Assume H2:
∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x3 x7 x8 = x3 x8 x7.
Assume H4:
∀ x7 . prim1 x7 x0 ⟶ x3 x1 x7 = x7.
Assume H6:
∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x4 x7 x8 = x4 x8 x7.
Assume H8: x2 = x1 ⟶ ∀ x7 : ο . x7.
Assume H9:
∀ x7 . prim1 x7 x0 ⟶ x4 x2 x7 = x7.
Assume H12:
∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ (λ x9 . prim0 (λ x10 . and (prim1 x10 x0) (∃ x11 . and (prim1 x11 x0) (x9 = x6 x10 x11)))) (x6 x7 x8) = x7.
Assume H13:
∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ (λ x9 . prim0 (λ x10 . and (prim1 x10 x0) (x9 = x6 ((λ x11 . prim0 (λ x12 . and (prim1 x12 x0) (∃ x13 . and (prim1 x13 x0) (x11 = x6 x12 x13)))) x9) x10))) (x6 x7 x8) = x8.