Let x0 of type ι be given.

Let x1 of type ι be given.

Assume H0: Inj0 x0 = Inj0 x1.

Apply Unj_Inj0_eq with x0, λ x2 x3 . x2 = x1.

Apply Unj_Inj0_eq with x1, λ x2 x3 . Unj (Inj0 x0) = x2.

Apply H0 with λ x2 x3 . Unj x3 = Unj (Inj0 x1).

Let x2 of type ι → ι → ο be given.

Assume H1: x2 (Unj (Inj0 x1)) (Unj (Inj0 x1)).

The subproof is completed by applying H1.

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Proofgold Proof