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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNoLev x0SNoLev x1.
Apply SNoS_I with SNoLev x1, x0, SNoLev x0 leaving 3 subgoals.
Apply SNoLev_ordinal with x1.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply SNoLev_ with x0.
The subproof is completed by applying H0.