Let x0 of type ι be given.

Let x1 of type ι be given.

Assume H0: prim1 x1 (prim3 x0).

Let x2 of type ο be given.

Assume H1: ∀ x3 . prim1 x1 x3 ⟶ prim1 x3 x0 ⟶ x2.

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

The subproof is completed by applying H0.

Let x3 of type ι be given.

Assume H2: (λ x4 . and (prim1 x1 x4) (prim1 x4 x0)) x3.

Apply H2 with x2.

The subproof is completed by applying H1 with x3.

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Proofgold Proof