const SNo : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_com: !x:set.!y:set.SNo x -> SNo y -> x + y = y + x const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const eps_ : set set const ordsucc : set set const In : set set prop term iIn = In infix iIn 2000 2000 const SNoLev : set set const omega : set const nat_p : set prop var x:set var y:set hyp nat_p x hyp x iIn omega hyp SNo (eps_ (ordsucc x)) hyp SNo y hyp SNoLev y iIn ordsucc (ordsucc x) hyp eps_ (ordsucc x) < y claim eps_ x < y + eps_ (ordsucc x) -> eps_ x < y + eps_ (ordsucc x) & eps_ x < eps_ (ordsucc x) + y