Let x0 of type ι be given.

Let x1 of type ι be given.

Assume H0: Inj1 x0 = Inj1 x1.

Apply Unj_Inj1_eq with x0, λ x2 x3 . x2 = x1.

Apply Unj_Inj1_eq with x1, λ x2 x3 . Unj (Inj1 x0) = x2.

Apply H0 with λ x2 x3 . Unj x3 = Unj (Inj1 x1).

Let x2 of type ι → ι → ο be given.

Assume H1: x2 (Unj (Inj1 x1)) (Unj (Inj1 x1)).

The subproof is completed by applying H1.

■

Proofgold Proof