const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const nat_p : set prop const omega : set axiom nat_p_omega: !x:set.nat_p x -> x iIn omega const SNoS_ : set set const ordsucc : set set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const Empty : set const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 const eps_ : set set lemma !x:set.!y:set.nat_p x -> y iIn SNoS_ (ordsucc (ordsucc x)) -> Empty < y -> x iIn omega -> eps_ x <= y claim !x:set.nat_p x -> !y:set.y iIn SNoS_ (ordsucc (ordsucc x)) -> Empty < y -> eps_ x <= y