Let x0 of type ι → (ι → (ι → ο) → ο) → (ι → ο) → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → (ι → ο) → ο . (∀ x4 . In x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x1 . 59843.. x0 x1 (c2908.. x0 x1).
Let x1 of type ι be given.
Apply Descr_Vo2_prop with
59843.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : (ι → ο) → ο . 59843.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (c2908.. x0).
Apply unknownprop_54227b2755ecfc6763a411886ac17934284ad0adefc285a218d3677cfe1ba03e with
x0,
x1,
c2908.. x0.
The subproof is completed by applying H1.
Apply unknownprop_241567373249cebe800ea93e957de3f6f50c9bec24c19d79ccfcdf8e1220e495 with
x0,
x1.
The subproof is completed by applying H0.