const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x const ordsucc : set set axiom nat_ordsucc: !x:set.nat_p x -> nat_p (ordsucc x) axiom nat_p_omega: !x:set.nat_p x -> x iIn omega claim !x:set.x iIn omega -> ordsucc x iIn omega