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 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 Empty : set axiom EmptyE: !x:set.nIn x Empty axiom FalseE: ~ False claim !x:set.(!y:set.y iIn x -> SNo y) -> (!y:set.y iIn Empty -> SNo y) & (!y:set.y iIn x -> SNo y) & !y:set.y iIn Empty -> !z:set.z iIn x -> y < z