const ordinal : set prop const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set const SNo : set prop axiom SNo_ordinal_ind: !p:set prop.(!x:set.ordinal x -> !y:set.y iIn SNoS_ x -> p y) -> !x:set.SNo x -> p x const SNoLev : set set var p:set prop hyp !x:set.SNo x -> (!y:set.y iIn SNoS_ (SNoLev x) -> p y) -> p x claim (!x:set.ordinal x -> !y:set.y iIn SNoS_ x -> p y) -> !x:set.SNo x -> p x