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.
Let x1 of type ι be given.
Apply unknownprop_241567373249cebe800ea93e957de3f6f50c9bec24c19d79ccfcdf8e1220e495 with
x0,
x1,
c2908.. x0 x1,
x0 x1 (c2908.. x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_2eda5698b3b9a6b7d85c38116cc10a00ac37dafd013986892ffc9041c9c79ce3 with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_f5273c2cd0419b3e99148d622522bd1b9adfdbbe4343730f84e1c348c832073e with
x0,
x1.
The subproof is completed by applying H0.