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 ordsucc : set set axiom ordinal_ordsucc: !x:set.ordinal x -> ordinal (ordsucc x) const SNo : set prop const SNoLev : set set const omega : set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 lemma !x:set.SNo x -> SNoLev x iIn omega -> ordinal (SNoLev x) -> ordinal (ordsucc (SNoLev x)) -> ?y:set.y iIn omega & x < y var x:set hyp SNo x hyp SNoLev x iIn omega claim ordinal (SNoLev x) -> ?y:set.y iIn omega & x < y