const ordinal : set prop const ordsucc : set set axiom ordinal_ordsucc: !x:set.ordinal x -> ordinal (ordsucc x) const PNoLt_pwise : (set (set prop) prop) (set (set prop) prop) prop const PNo_lenbdd : set (set (set prop) prop) prop const In : set set prop term iIn = In infix iIn 2000 2000 const PNo_rel_strict_split_imv : (set (set prop) prop) (set (set prop) prop) set (set prop) prop axiom PNo_rel_imv_bdd_ex: !P:set (set prop) prop.!Q:set (set prop) prop.PNoLt_pwise P Q -> !x:set.ordinal x -> PNo_lenbdd x P -> PNo_lenbdd x Q -> ?y:set.y iIn ordsucc x & ?p:set prop.PNo_rel_strict_split_imv P Q y p const PNo_strict_imv : (set (set prop) prop) (set (set prop) prop) set (set prop) prop lemma !P:set (set prop) prop.!Q:set (set prop) prop.!x:set.!y:set.!p:set prop.ordinal x -> y iIn ordsucc x -> PNo_rel_strict_split_imv P Q y p -> ordinal (ordsucc x) -> ?z:set.z iIn ordsucc x & ?q:set prop.PNo_strict_imv P Q z q claim !P:set (set prop) prop.!Q:set (set prop) prop.PNoLt_pwise P Q -> !x:set.ordinal x -> PNo_lenbdd x P -> PNo_lenbdd x Q -> ?y:set.y iIn ordsucc x & ?p:set prop.PNo_strict_imv P Q y p