const In : set set prop term iIn = In infix iIn 2000 2000 const PNo_upc : (set (set prop) prop) set (set prop) prop const PNoLt : set (set prop) set (set prop) prop term PNo_rel_strict_lowerbd = \P:set (set prop) prop.\x:set.\p:set prop.!y:set.y iIn x -> !q:set prop.PNo_upc P y q -> PNoLt x p y q const PNoEq_ : set (set prop) (set prop) prop axiom PNoEq_sym_: !x:set.!p:set prop.!q:set prop.PNoEq_ x p q -> PNoEq_ x q p const ordinal : set prop axiom PNoEqLt_tra: !x:set.!y:set.ordinal x -> ordinal y -> !p:set prop.!q:set prop.!p2:set prop.PNoEq_ x p q -> PNoLt x q y p2 -> PNoLt x p y p2 var P:set (set prop) prop var x:set var p:set prop var q:set prop var y:set var p2:set prop hyp ordinal x hyp PNoEq_ x p q hyp PNo_rel_strict_lowerbd P x p hyp y iIn x hyp PNo_upc P y p2 claim ordinal y -> PNoLt x q y p2