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Proofgold Proof

pf
Let x0 of type ιι be given.
Let x1 of type ιι be given.
Let x2 of type ι be given.
Assume H0: x0 = x1.
Assume H1: x0 x2 = x1 x2False.
Apply H1.
Apply H0 with λ x3 x4 : ι → ι . x4 x2 = x1 x2.
Let x3 of type ιιο be given.
Assume H2: x3 (x1 x2) (x1 x2).
The subproof is completed by applying H2.