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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 ∈ SNoLev x0.
Claim L2: ordinal x1
Apply ordinal_Hered with SNoLev x0, x1 leaving 2 subgoals.
Apply SNoLev_ordinal with x0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Claim L3: SNo_ x1 (binintersect x0 (SNoElts_ x1))
Apply restr_SNo_ with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNoLev_uniq2 with x1, binintersect x0 (SNoElts_ x1) leaving 2 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying L3.
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