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Proofgold Proof

pf
Let x0 of type ι((ιο) → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type (ιο) → ο be given.
Assume H0: ∀ x3 : (ι → ο) → ο . (∀ x4 : ι → ο . (∀ x5 . x4 x5prim1 x5 x1)iff (x2 x4) (x3 x4))x0 x1 x3 = x0 x1 x2.
Apply unknownprop_73cbfbefa0026020cb29acf19575c6895e982d80894689a2eefd5ca0f4010f05 with x1, x2, λ x3 x4 . x0 x3 (decode_c (f482f.. (35104.. x1 x2) (4ae4a.. 4a7ef..))) = x0 x1 x2.
Apply H0 with decode_c (f482f.. (35104.. x1 x2) (4ae4a.. 4a7ef..)).
Let x3 of type ιο be given.
Assume H1: ∀ x4 . x3 x4prim1 x4 x1.
Apply unknownprop_a43e2c960a060cf2cbb41d55511fc48d292b3f138aadca7f276be3ed64c8fb26 with x1, x2, x3, λ x4 x5 : ο . iff (x2 x3) x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x3.