const ordinal : set prop const omega : set axiom omega_ordinal: ordinal omega const In : set set prop term iIn = In infix iIn 2000 2000 const ordsucc : set set axiom omega_ordsucc: !x:set.x iIn omega -> ordsucc x iIn omega const SNo_ : set set prop const eps_ : set set axiom SNo__eps_: !x:set.x iIn omega -> SNo_ (ordsucc x) (eps_ x) const SNoS_ : set set axiom SNoS_I: !x:set.ordinal x -> !y:set.!z:set.z iIn x -> SNo_ z y -> y iIn SNoS_ x claim !x:set.x iIn omega -> eps_ x iIn SNoS_ omega