const PNoLe : set (set prop) set (set prop) prop const SNoLev : set set const In : set set prop term iIn = In infix iIn 2000 2000 term SNoLe = \x:set.\y:set.PNoLe (SNoLev x) (\z:set.z iIn x) (SNoLev y) \z:set.z iIn y term <= = SNoLe infix <= 2020 2020 const PNoLt : set (set prop) set (set prop) prop term SNoLt = \x:set.\y:set.PNoLt (SNoLev x) (\z:set.z iIn x) (SNoLev y) \z:set.z iIn y term < = SNoLt infix < 2020 2020 axiom PNoLeI1: !x:set.!y:set.!p:set prop.!q:set prop.PNoLt x p y q -> PNoLe x p y q claim !x:set.!y:set.x < y -> x <= y