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

Let x1 of type ι be given.

Let x2 of type ι → ι → ι be given.

Let x3 of type ι → ι be given.

Assume H0: ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x3 x6 = x5 x6) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3.

Apply unknownprop_0de249c9a6cc0d3bcd5cc89147ea799acb4f233823c55edb760ffe9d4ffc7a91 with x1, x2, x3, λ x4 x5 . x0 x4 (e3162.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3.

Apply H0 with e3162.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. 4a7ef..)), f482f.. (f482f.. (971d3.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.

The subproof is completed by applying unknownprop_6a5674efb6b0d571fb24cd5f7a30b471eec1bdac0d350bb303a07726f30cd6bf with x1, x2, x3.

The subproof is completed by applying unknownprop_8107478b497c3b04aa44623f19e37dac344de98a93384327865b5df8b8117888 with x1, x2, x3.

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Proofgold Proof