const ordinal : set prop const In : set set prop term iIn = In infix iIn 2000 2000 axiom ordinal_ind: !p:set prop.(!x:set.ordinal x -> (!y:set.y iIn x -> p y) -> p x) -> !x:set.ordinal x -> p x axiom dneg: !P:prop.~ ~ P -> P lemma !p:set prop.(?x:set.ordinal x & p x) -> ~ (?x:set.ordinal x & p x & !y:set.y iIn x -> ~ p y) -> ~ !x:set.ordinal x -> ~ p x claim !p:set prop.(?x:set.ordinal x & p x) -> ?x:set.ordinal x & p x & !y:set.y iIn x -> ~ p y