const SNo : set prop const ordinal : set prop const SNoLev : set set axiom SNoLev_ordinal: !x:set.SNo x -> ordinal (SNoLev x) const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set lemma !r:set set prop.!x:set.!y:set.(!z:set.ordinal z -> !w:set.ordinal w -> !u:set.u iIn SNoS_ z -> !v:set.v iIn SNoS_ w -> r u v) -> SNo x -> SNo y -> ordinal (SNoLev x) -> r x y claim !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