const PNo_rel_strict_upperbd : (set (set prop) prop) set (set prop) prop const PNo_rel_strict_lowerbd : (set (set prop) prop) set (set prop) prop term PNo_rel_strict_imv = \P:set (set prop) prop.\Q:set (set prop) prop.\x:set.\p:set prop.PNo_rel_strict_upperbd P x p & PNo_rel_strict_lowerbd Q x p const PNo_strict_upperbd : (set (set prop) prop) set (set prop) prop const PNo_strict_lowerbd : (set (set prop) prop) set (set prop) prop term PNo_strict_imv = \P:set (set prop) prop.\Q:set (set prop) prop.\x:set.\p:set prop.PNo_strict_upperbd P x p & PNo_strict_lowerbd Q x p const ordinal : set prop const In : set set prop term iIn = In infix iIn 2000 2000 const ordsucc : set set axiom PNo_strict_upperbd_imp_rel_strict_upperbd: !P:set (set prop) prop.!x:set.ordinal x -> !y:set.y iIn ordsucc x -> !p:set prop.PNo_strict_upperbd P x p -> PNo_rel_strict_upperbd P y p axiom PNo_strict_lowerbd_imp_rel_strict_lowerbd: !P:set (set prop) prop.!x:set.ordinal x -> !y:set.y iIn ordsucc x -> !p:set prop.PNo_strict_lowerbd P x p -> PNo_rel_strict_lowerbd P y p claim !P:set (set prop) prop.!Q:set (set prop) prop.!x:set.ordinal x -> !y:set.y iIn ordsucc x -> !p:set prop.PNo_strict_imv P Q x p -> PNo_rel_strict_upperbd P y p & PNo_rel_strict_lowerbd Q y p