const In : set set prop term iIn = In infix iIn 2000 2000 const Subq : set set prop term TransSet = \x:set.!y:set.y iIn x -> Subq y x term ordinal = \x:set.TransSet x & !y:set.y iIn x -> TransSet y const binintersect : set set set axiom ordinal_binintersect: !x:set.!y:set.ordinal x -> ordinal y -> ordinal (binintersect x y) const PNoLt : set (set prop) set (set prop) prop const PNoEq_ : set (set prop) (set prop) prop lemma !x:set.!y:set.!p:set prop.!q:set prop.ordinal x -> ordinal y -> TransSet x -> TransSet y -> ordinal (binintersect x y) -> PNoLt x p y q | x = y & PNoEq_ x p q | PNoLt y q x p claim !x:set.!y:set.!p:set prop.!q:set prop.ordinal x -> ordinal y -> PNoLt x p y q | x = y & PNoEq_ x p q | PNoLt y q x p