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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Apply SNo_SNo with ordsucc (SNoLev x0), SNo_extend1 x0 leaving 2 subgoals.
Apply ordinal_ordsucc with SNoLev x0.
Apply SNoLev_ordinal with x0.
The subproof is completed by applying H0.
Apply SNo_extend1_SNo_ with x0.
The subproof is completed by applying H0.