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