const SNo : set prop const ordinal : set prop const SNoLev : set set axiom SNoLev_ordinal: !x:set.SNo x -> ordinal (SNoLev x) const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set lemma !p:set prop.!x:set.(!y:set.ordinal y -> !z:set.z iIn SNoS_ y -> p z) -> SNo x -> ordinal (SNoLev x) -> p x claim !p:set prop.(!x:set.ordinal x -> !y:set.y iIn SNoS_ x -> p y) -> !x:set.SNo x -> p x