const PNoLt : set (set prop) set (set prop) prop const PNoEq_ : set (set prop) (set prop) prop term PNoLe = \x:set.\p:set prop.\y:set.\q:set prop.PNoLt x p y q | x = y & PNoEq_ x p q const ordinal : set prop axiom PNoEqLe_tra: !x:set.!y:set.ordinal x -> ordinal y -> !p:set prop.!q:set prop.!p2:set prop.PNoEq_ x p q -> PNoLe x q y p2 -> PNoLe x p y p2 var x:set var y:set var z:set var p:set prop var q:set prop var p2:set prop hyp ordinal y hyp ordinal z hyp PNoLe y q z p2 hyp x = y hyp PNoEq_ x p q claim PNoEq_ y p q -> PNoLe y p z p2