Let x0 of type ι → (ι → ι) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Assume H0:
∀ x3 : ι → ι . (∀ x4 . prim1 x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x3 = x0 x1 x2.
Apply unknownprop_64b30c93b63a275b33e0b1e088688090a219594d60d94e87e633646df8931180 with
x1,
x2,
λ x3 x4 . x0 x3 (f482f.. (f482f.. (c0301.. x1 x2) (4ae4a.. 4a7ef..))) = x0 x1 x2.
Apply H0 with
f482f.. (f482f.. (c0301.. x1 x2) (4ae4a.. 4a7ef..)).
Let x3 of type ι be given.
Apply unknownprop_f58b95d170c532b1a6ac682a4e91de3a8560ab9616f3c2e2f8b45045ae40523f with
x1,
x2,
x3.
The subproof is completed by applying H1.