const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const ordinal : set prop const PNo_strict_imv : (set (set prop) prop) (set (set prop) prop) set (set prop) prop term PNo_least_rep = \P:set (set prop) prop.\Q:set (set prop) prop.\x:set.\p:set prop.ordinal x & PNo_strict_imv P Q x p & !y:set.y iIn x -> !q:set prop.~ PNo_strict_imv P Q y q term PNo_least_rep2 = \P:set (set prop) prop.\Q:set (set prop) prop.\x:set.\p:set prop.PNo_least_rep P Q x p & !y:set.nIn y x -> ~ p y term PNoEq_ = \x:set.\p:set prop.\q:set prop.!y:set.y iIn x -> (p y <-> q y) axiom ordinal_Hered: !x:set.ordinal x -> !y:set.y iIn x -> ordinal y const ordsucc : set set var P:set (set prop) prop var Q:set (set prop) prop var x:set var y:set var p:set prop hyp ordinal x hyp y iIn ordsucc x hyp PNo_strict_imv P Q y p claim ordinal (ordsucc x) -> ?z:set.ordinal z & ?q:set prop.PNo_strict_imv P Q z q