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Proofgold Proof

pf
Let x0 of type ι(ι(ιο) → ο) → (ιο) → ο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → (ι → ο) → ο . (∀ x4 . In x4 x1x2 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.