const binunion : set set set const Sep : set (set prop) set const ReplSep : set (set prop) (set set) set const SetAdjoin : set set set const Sing : set set const ordsucc : set set const Empty : set term PSNo = \x:set.\p:set prop.binunion (Sep x p) (ReplSep x (\y:set.~ p y) \y:set.SetAdjoin y (Sing (ordsucc Empty))) const SNoLev : set set const In : set set prop term iIn = In infix iIn 2000 2000 term SNo_extend1 = \x:set.PSNo (ordsucc (SNoLev x)) \y:set.y iIn x | y = SNoLev x axiom ordsuccI2: !x:set.x iIn ordsucc x axiom SepI: !x:set.!p:set prop.!y:set.y iIn x -> p y -> y iIn Sep x p axiom binunionI1: !x:set.!y:set.!z:set.z iIn x -> z iIn binunion x y const SNo : set prop claim !x:set.SNo x -> SNoLev x iIn SNo_extend1 x