Let x0 of type ι → (ι → ι → ο) → ι → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ι → ο . (∀ x4 . In x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Let x1 of type ι be given.
Apply unknownprop_b770534102bad575dcc908ba2bd3be3cd352ae4c3095917d5f34873a1d6be083 with
x0,
x1,
f9c5e.. x0 x1,
x0 x1 (f9c5e.. x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_33d3425701b53c0a6330607b14fbeb2cf0a994c3f62ac0cf25e89ab42e5460f2 with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_ae3dac4b88b9de273e6ab26de0d6cb59f2e5a62ec0d064363064384e394a797a with
x0,
x1.
The subproof is completed by applying H0.