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_ind3: !P:set set set prop.(!x:set.ordinal x -> !y:set.ordinal y -> !z:set.ordinal z -> !w:set.w iIn SNoS_ x -> !u:set.u iIn SNoS_ y -> !v:set.v iIn SNoS_ z -> P w u v) -> !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> P x y z const SNoLev : set set var P:set set set prop hyp !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> (!w:set.w iIn SNoS_ (SNoLev x) -> P w y z) -> (!w:set.w iIn SNoS_ (SNoLev y) -> P x w z) -> (!w:set.w iIn SNoS_ (SNoLev z) -> P x y w) -> (!w:set.w iIn SNoS_ (SNoLev x) -> !u:set.u iIn SNoS_ (SNoLev y) -> P w u z) -> (!w:set.w iIn SNoS_ (SNoLev x) -> !u:set.u iIn SNoS_ (SNoLev z) -> P w y u) -> (!w:set.w iIn SNoS_ (SNoLev y) -> !u:set.u iIn SNoS_ (SNoLev z) -> P x w u) -> (!w:set.w iIn SNoS_ (SNoLev x) -> !u:set.u iIn SNoS_ (SNoLev y) -> !v:set.v iIn SNoS_ (SNoLev z) -> P w u v) -> P x y z claim (!x:set.ordinal x -> !y:set.ordinal y -> !z:set.ordinal z -> !w:set.w iIn SNoS_ x -> !u:set.u iIn SNoS_ y -> !v:set.v iIn SNoS_ z -> P w u v) -> !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> P x y z