const ordinal : set prop const In : set set prop term iIn = In infix iIn 2000 2000 axiom ordinal_Hered: !x:set.ordinal x -> !y:set.y iIn x -> ordinal y const SNoS_ : set set const SNo_ : set set prop axiom SNoS_E: !x:set.ordinal x -> !y:set.y iIn SNoS_ x -> ?z:set.z iIn x & SNo_ z y const SNoLev : set set const SNo : set prop lemma !x:set.!y:set.!P:prop.!z:set.ordinal x -> (SNoLev y iIn x -> ordinal (SNoLev y) -> SNo y -> SNo_ (SNoLev y) y -> P) -> z iIn x -> SNo_ z y -> ordinal z -> P claim !x:set.ordinal x -> !y:set.y iIn SNoS_ x -> !P:prop.(SNoLev y iIn x -> ordinal (SNoLev y) -> SNo y -> SNo_ (SNoLev y) y -> P) -> P