const PNoLt : set (set prop) set (set prop) prop const SNoLev : set set const In : set set prop term iIn = In infix iIn 2000 2000 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 const PNoEq_ : set (set prop) (set prop) prop term SNoEq_ = \x:set.\y:set.\z:set.PNoEq_ x (\w:set.w iIn y) \w:set.w iIn z axiom PNoLtI2: !x:set.!y:set.!p:set prop.!q:set prop.x iIn y -> PNoEq_ x p q -> q x -> PNoLt x p y q claim !x:set.!y:set.SNoLev x iIn SNoLev y -> SNoEq_ (SNoLev x) x y -> SNoLev x iIn y -> x < y