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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Apply SNoLtI3 with SNo_extend0 x0, x0 leaving 3 subgoals.
Apply SNo_extend0_SNoLev with x0, λ x1 x2 . SNoLev x0x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying ordsuccI2 with SNoLev x0.
Apply SNo_extend0_SNoEq with x0.
The subproof is completed by applying H0.
Apply SNo_extend0_nIn with x0.
The subproof is completed by applying H0.