const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y term TransSet = \x:set.!y:set.y iIn x -> Subq y x const PNoEq_ : set (set prop) (set prop) prop term PNoLt_ = \x:set.\p:set prop.\q:set prop.?y:set.y iIn x & (PNoEq_ y p q & ~ p y & q y) term ordinal = \x:set.TransSet x & !y:set.y iIn x -> TransSet y claim !p:set prop.!q:set prop.!x:set.ordinal x -> !y:set.y iIn x -> PNoLt_ y p q -> ?z:set.z iIn x & (PNoEq_ z p q & ~ p z & q z)