const In : set set prop term iIn = In infix iIn 2000 2000 term PNoEq_ = \x:set.\p:set prop.\q:set prop.!y:set.y iIn x -> (p y <-> q y) term SNoEq_ = \x:set.\y:set.\z:set.PNoEq_ x (\w:set.w iIn y) \w:set.w iIn z 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 axiom SNo_eq: !x:set.!y:set.SNo x -> SNo y -> SNoLev x = SNoLev y -> SNoEq_ (SNoLev x) x y -> x = y claim !x:set.SNo x -> SNoLev x = Empty -> x = Empty