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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: ∀ x1 . x1x0SNo x1.
Apply and3I with ∀ x1 . x10SNo x1, ∀ x1 . x1x0SNo x1, ∀ x1 . x10∀ x2 . x2x0SNoLt x1 x2 leaving 3 subgoals.
Let x1 of type ι be given.
Assume H1: x10.
Apply FalseE with SNo x1.
Apply EmptyE with x1.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Let x1 of type ι be given.
Assume H1: x10.
Apply FalseE with ∀ x2 . x2x0SNoLt x1 x2.
Apply EmptyE with x1.
The subproof is completed by applying H1.