const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const SNo : set prop const Empty : set axiom SNo_0: SNo Empty const SNoLev : set set axiom SNoLev_0: SNoLev Empty = Empty axiom EmptyE: !x:set.nIn x Empty axiom FalseE: ~ False const SNoEq_ : set set set prop axiom SNoEq_I: !x:set.!y:set.!z:set.(!w:set.w iIn x -> (w iIn y <-> w iIn z)) -> SNoEq_ x y z axiom SNo_eq: !x:set.!y:set.SNo x -> SNo y -> SNoLev x = SNoLev y -> SNoEq_ (SNoLev x) x y -> x = y const SNoCut : set set set const ordsucc : set set hyp SNo (SNoCut Empty Empty) hyp SNoLev (SNoCut Empty Empty) iIn ordsucc Empty claim SNoLev (SNoCut Empty Empty) = Empty -> SNoCut Empty Empty = Empty