const TransSet : set prop const In : set set prop term iIn = In infix iIn 2000 2000 term ordinal = \x:set.TransSet x & !y:set.y iIn x -> TransSet y const omega : set axiom omega_TransSet: TransSet 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 axiom ordinal_TransSet: !x:set.ordinal x -> TransSet x claim TransSet omega & !x:set.x iIn omega -> TransSet x