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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Assume H1: ∀ x1 . x1SNoS_ (SNoLev x0)SNoLt x1 x0.
Apply SNo_max_SNoLev with x0, λ x1 x2 . ordinal x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNoLev_ordinal with x0.
The subproof is completed by applying H0.