const In : set set prop term iIn = In infix iIn 2000 2000 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) claim !x:set.!p:set prop.!q:set prop.PNoLt_ x p q -> !P:prop.(!y:set.y iIn x -> PNoEq_ y p q -> ~ p y -> q y -> P) -> P