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