const SNo : set prop const Empty : set axiom SNo_0: SNo Empty const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const eps_ : set set axiom SNo_eps_: !x:set.x iIn omega -> SNo (eps_ x) const SNoLt : set set prop term < = SNoLt infix < 2020 2020 axiom SNo_eps_pos: !x:set.x iIn omega -> Empty < eps_ x const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_Lt2: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> y < z -> (x + y) < x + z axiom add_SNo_0R: !x:set.SNo x -> x + Empty = x claim !x:set.SNo x -> !y:set.y iIn omega -> x < x + eps_ y