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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Apply SNoLev_prop with x0, x0 ∈ SNoS_ (ordsucc (SNoLev x0)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: ordinal (SNoLev x0).
Assume H2: SNo_ (SNoLev x0) x0.
Apply SNoS_I with ordsucc (SNoLev x0), x0, SNoLev x0 leaving 3 subgoals.
Apply ordinal_ordsucc with SNoLev x0.
The subproof is completed by applying H1.
The subproof is completed by applying ordsuccI2 with SNoLev x0.
The subproof is completed by applying H2.
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