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 → ι → ι be given.
Let x5 of type ι → ι → ι be given.
Let x6 of type ι → ι → ι be given.
Let x7 of type ι → ι be given.
Let x8 of type ι → ι be given.
Assume H0:
∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x1 x9 x10 = x2 x9 x10.
Assume H1:
∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x3 x9 x10 = x4 x9 x10.
Assume H2:
∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x5 x9 x10 = x6 x9 x10.
Assume H3:
∀ x9 . prim1 x9 x0 ⟶ x7 x9 = x8 x9.