const In : set set prop term iIn = In infix iIn 2000 2000 const UnivOf : set set axiom UnivOf_In: !x:set.x iIn UnivOf x const ZF_closed : set prop axiom UnivOf_ZF_closed: !x:set.ZF_closed (UnivOf x) const ordsucc : set set axiom ZF_ordsucc_closed: !x:set.ZF_closed x -> !y:set.y iIn x -> ordsucc y iIn x const Empty : set const nat_p : set prop axiom nat_ind: !p:set prop.p Empty -> (!x:set.nat_p x -> p x -> p (ordsucc x)) -> !x:set.nat_p x -> p x claim !x:set.nat_p x -> x iIn UnivOf Empty