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