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_ind2: !r:set set prop.(!x:set.ordinal x -> !y:set.ordinal y -> !z:set.z iIn SNoS_ x -> !w:set.w iIn SNoS_ y -> r z w) -> !x:set.!y:set.SNo x -> SNo y -> r x y const SNoLev : set set var r:set set prop hyp !x:set.!y:set.SNo x -> SNo y -> (!z:set.z iIn SNoS_ (SNoLev x) -> r z y) -> (!z:set.z iIn SNoS_ (SNoLev y) -> r x z) -> (!z:set.z iIn SNoS_ (SNoLev x) -> !w:set.w iIn SNoS_ (SNoLev y) -> r z w) -> r x y claim (!x:set.ordinal x -> !y:set.ordinal y -> !z:set.z iIn SNoS_ x -> !w:set.w iIn SNoS_ y -> r z w) -> !x:set.!y:set.SNo x -> SNo y -> r x y