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 SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 const Empty : set const eps_ : set set const ordsucc : set set const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 var x:set var y:set hyp x iIn omega hyp SNo (eps_ (ordsucc x)) hyp SNo y hyp y <= Empty claim (y + eps_ (ordsucc x)) < eps_ x -> (y + eps_ (ordsucc x)) < eps_ x & (eps_ (ordsucc x) + y) < eps_ x