Let x0 of type ι be given.

Let x1 of type ι → ι be given.

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

Let x2 of type ι be given.

Assume H1: prim1 x2 x0.

Let x3 of type ι → ο be given.

Assume H2: ∀ x4 . ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x4 ⟶ prim1 (x5 x6) x4) ⟶ ∀ x6 . prim1 x6 x4 ⟶ x3 (8eacd.. x4 x5 x6).

Apply H2 with x0, x1, x2 leaving 2 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

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Proofgold Proof