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 SNoLev : set set const eps_ : set set const ordsucc : set set lemma !x:set.x iIn omega -> nat_p x -> SNoLev (eps_ x) = ordsucc x claim !x:set.x iIn omega -> SNoLev (eps_ x) = ordsucc x