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