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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Let x1 of type ι be given.
Assume H1: x1 ∈ SNoS_ (SNoLev x0).
Assume H2: x1 = x0.
Apply SNoLev_prop with x0, False leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H3: ordinal (SNoLev x0).
Assume H4: SNo_ (SNoLev x0) x0.
Apply SNoS_E2 with SNoLev x0, x1, False leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H1.
Assume H5: SNoLev x1 ∈ SNoLev x0.
Assume H6: ordinal (SNoLev x1).
Assume H7: SNo x1.
Assume H8: SNo_ (SNoLev x1) x1.
Apply In_irref with SNoLev x1.
Apply H2 with λ x2 x3 . SNoLev x1 ∈ SNoLev x3.
The subproof is completed by applying H5.
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