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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιι be given.
Let x3 of type ιι be given.
Let x4 of type ι be given.
Apply Unj_Inj1_eq with x4, λ x5 x6 . If_i (Inj1 x4 = Inj0 x6) (x2 x6) (x3 x6) = x3 x4.
Apply If_i_0 with Inj1 x4 = Inj0 x4, x2 x4, x3 x4.
Assume H0: Inj1 x4 = Inj0 x4.
Apply Inj0_Inj1_neq with x4, x4.
Let x5 of type ιιο be given.
The subproof is completed by applying H0 with λ x6 x7 . x5 x7 x6.