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 nat_p : set prop const ordsucc : set set const Empty : set axiom nat_1: nat_p (ordsucc Empty) const omega : set axiom nat_p_omega: !x:set.nat_p x -> x iIn omega const SNoS_ : set set axiom omega_SNoS_omega: Subq omega (SNoS_ omega) const real : set axiom SNoS_omega_real: Subq (SNoS_ omega) real claim ordsucc Empty iIn real