const ordinal : set prop const SNo_ : set set prop const SNoLev : set set axiom SNoLev_uniq2: !x:set.ordinal x -> !y:set.SNo_ x y -> SNoLev y = x const SNo : set prop axiom SNoLev_prop: !x:set.SNo x -> ordinal (SNoLev x) & SNo_ (SNoLev x) x const In : set set prop term iIn = In infix iIn 2000 2000 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 -> ordinal (SNoLev y) -> SNo_ (SNoLev y) y -> SNoLev y = z -> P var x:set var y:set var P:prop var z:set hyp SNoLev y iIn x -> ordinal (SNoLev y) -> SNo y -> SNo_ (SNoLev y) y -> P hyp z iIn x hyp SNo_ z y hyp ordinal z claim SNo y -> P