Let x0 of type ι → (ι → ι → ι → ο) → ι → ι → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → 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_f1193b6d6ed98f53e20a7c2c98b95043e1d349df91d36c172d7f2aee2f50f66e with
x0,
x1,
03431.. x0 x1,
x0 x1 (03431.. x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_8e68c9bc75c52abb5b98f9837a4e82ff174486408a6cae70354475efbe32f58f with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_4abd2c46bb9d2d5f87958a10801820c9054a8c60847a86da45accb5913f17fad with
x0,
x1.
The subproof is completed by applying H0.