Let x0 of type ι → (ι → ((ι → ο) → ο) → ο) → ((ι → ο) → ο) → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ((ι → ο) → 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_f8e298c212ecb25f425f9e64ca55910b86e06fb1674aefb60326d44f370d161e with
x0,
x1,
2bbaf.. x0 x1,
x0 x1 (2bbaf.. x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_8e085b788604157bcaa930259dfea85aa34fe4f40585a51b4e841cc85ff14f0a with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_7d13e2608f735f9ad9055e8c8dc20b1cd786ad52828056d02d9d5d8fef3d9417 with
x0,
x1.
The subproof is completed by applying H0.