const SNoCutP : set set prop const SNo : set prop const SNoCut : set set set const In : set set prop term iIn = In infix iIn 2000 2000 const SNoLev : set set const ordsucc : set set const binunion : set set set const famunion : set (set set) set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const Subq : set set prop const SNoEq_ : set set set prop axiom SNoCutP_SNoCut: !x:set.!y:set.SNoCutP x y -> SNo (SNoCut x y) & SNoLev (SNoCut x y) iIn ordsucc (binunion (famunion x \z:set.ordsucc (SNoLev z)) (famunion y \z:set.ordsucc (SNoLev z))) & (!z:set.z iIn x -> z < SNoCut x y) & (!z:set.z iIn y -> SNoCut x y < z) & !z:set.SNo z -> (!w:set.w iIn x -> w < z) -> (!w:set.w iIn y -> z < w) -> Subq (SNoLev (SNoCut x y)) (SNoLev z) & SNoEq_ (SNoLev (SNoCut x y)) (SNoCut x y) z claim !x:set.!y:set.SNoCutP x y -> !z:set.z iIn x -> z < SNoCut x y