Let x0 of type ι → (ι → ι) → ι → ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι be given.

Let x3 of type ι be given.

Assume H0: ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x1 ⟶ x2 x5 = x4 x5) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3.

Apply unknownprop_128401b26ca0bc08d54bfca9904ebdbf186db1274a4be846be9a9cc30eb990c9 with x1, x2, x3, λ x4 x5 . x0 x4 (f482f.. (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) = x0 x1 x2 x3.

Apply unknownprop_e852dd30a45cb3a8cce74800ccca965088221e00f4794a6d5a0a5270b65d5a2a with x1, x2, x3, λ x4 x5 . x0 x1 (f482f.. (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4 = x0 x1 x2 x3.

Apply H0 with f482f.. (f482f.. (8eacd.. x1 x2 x3) (4ae4a.. 4a7ef..)).

The subproof is completed by applying unknownprop_185dfaf856c8b7f2b4591a434b0b04e8904e3e58c14681f42a4c6a9bacc9a6c3 with x1, x2, x3.

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Proofgold Proof