Let x0 of type ι be given.

Let x1 of type ι → ι be given.

Let x2 of type ι be given.

Assume H0: prim1 x2 (a842e.. x0 (λ x3 . x1 x3)).

Let x3 of type ο be given.

Assume H1: ∀ x4 . prim1 x4 x0 ⟶ prim1 x2 (x1 x4) ⟶ x3.

Apply unknownprop_6e713ef2b1c9d2089dead8e3d98fed6bda91ffc6b807ed8732c89724a15f5c2c with x0, x1, x2, x3 leaving 2 subgoals.

The subproof is completed by applying H0.

Let x4 of type ι be given.

Assume H2: (λ x5 . and (prim1 x5 x0) (prim1 x2 (x1 x5))) x4.

Apply H2 with x3.

The subproof is completed by applying H1 with x4.

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Proofgold Proof