const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const ordinal : set prop const omega : set axiom omega_ordinal: ordinal omega const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x axiom nat_p_ordinal: !x:set.nat_p x -> ordinal x const SNo : set prop axiom omega_SNo: !x:set.x iIn omega -> SNo x const SNo_ : set set prop const SNoLev : set set axiom SNoLev_: !x:set.SNo x -> SNo_ (SNoLev x) x axiom ordinal_SNoLev: !x:set.ordinal x -> SNoLev x = 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 -> x iIn SNoS_ omega