const ordinal : set prop const SNo_ : set set prop const SNo : set prop axiom SNo_SNo: !x:set.ordinal x -> !y:set.SNo_ x y -> SNo y const In : set set prop term iIn = In infix iIn 2000 2000 const SNoLev : set set lemma !x:set.!y:set.!P:prop.!z:set.(SNoLev y iIn x -> ordinal (SNoLev y) -> SNo y -> SNo_ (SNoLev y) y -> P) -> z iIn x -> SNo_ z y -> ordinal z -> SNo y -> P var x:set var y:set var P:prop var z:set hyp ordinal x hyp SNoLev y iIn x -> ordinal (SNoLev y) -> SNo y -> SNo_ (SNoLev y) y -> P hyp z iIn x hyp SNo_ z y claim ordinal z -> P