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 PNoEq_ : set (set prop) (set prop) prop const binintersect : set set set const PNoLt : set (set prop) set (set prop) prop lemma !x:set.!y:set.!p:set prop.!q:set prop.PNoEq_ (binintersect x y) p q -> x iIn y -> binintersect x y = x -> PNoEq_ x p q -> PNoLt x p y q | x = y & PNoEq_ x p q | PNoLt y q x p var x:set var y:set var p:set prop var q:set prop hyp TransSet y hyp PNoEq_ (binintersect x y) p q hyp x iIn y claim binintersect x y = x -> PNoLt x p y q | x = y & PNoEq_ x p q | PNoLt y q x p