Let x0 of type ι be given.

Let x1 of type ι → ι → ι be given.

Assume H0: ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0.

Let x2 of type ι → ο be given.

Assume H1: ∀ x3 . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x3 ⟶ ∀ x6 . prim1 x6 x3 ⟶ prim1 (x4 x5 x6) x3) ⟶ x2 (987b2.. x3 x4).

Apply H1 with x0, x1.

The subproof is completed by applying H0.

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Proofgold Proof