Let x0 of type ι → (ι → ι → ι) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Assume H0:
∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = x3 x4 x5) ⟶ x0 x1 x3 = x0 x1 x2.
Apply unknownprop_8674365f14b0285b3312b4875395e693d6df9b10fe9756f39519b30aacbeca91 with
x1,
x2,
λ x3 x4 . x0 x3 (e3162.. (f482f.. (987b2.. x1 x2) (4ae4a.. 4a7ef..))) = x0 x1 x2.
Apply H0 with
e3162.. (f482f.. (987b2.. x1 x2) (4ae4a.. 4a7ef..)).
Let x3 of type ι be given.
Let x4 of type ι be given.
Apply unknownprop_a59155e51c734938987e2b9ffb79da15884213566add9a57beb57783508c1eb2 with
x1,
x2,
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.