const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const ordinal : set prop const SNo : set prop axiom ordinal_SNo: !x:set.ordinal x -> SNo x const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const SNoLev : set set const omega : set lemma !x:set.!y:set.SNo x -> SNo y -> x < y -> SNoLev y iIn omega -> ordinal (SNoLev y) -> SNo (SNoLev y) -> ?z:set.z iIn omega & x < z var x:set var y:set hyp SNo x hyp SNo y hyp x < y hyp SNoLev y iIn omega claim ordinal (SNoLev y) -> ?z:set.z iIn omega & x < z