const In : set set prop term iIn = In infix iIn 2000 2000 const SNo : set prop const SNoLt : set set prop term < = SNoLt infix < 2020 2020 term SNoCutP = \x:set.\y:set.(!z:set.z iIn x -> SNo z) & (!z:set.z iIn y -> SNo z) & !z:set.z iIn x -> !w:set.w iIn y -> z < w const SNoLev : set set const SNoCut : set set set axiom SNo_etaE: !x:set.SNo x -> !P:prop.(!y:set.!z:set.SNoCutP y z -> (!w:set.w iIn y -> SNoLev w iIn SNoLev x) -> (!w:set.w iIn z -> SNoLev w iIn SNoLev x) -> x = SNoCut y z -> P) -> P const ordinal : set prop var p:set prop var x:set var y:set hyp !z:set.!w:set.SNoCutP z w -> (!u:set.u iIn z -> p u) -> (!u:set.u iIn w -> p u) -> p (SNoCut z w) hyp !z:set.z iIn x -> !w:set.SNo w -> SNoLev w iIn z -> p w hyp SNo y hyp SNoLev y iIn x claim ordinal (SNoLev y) -> p y