const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const Empty : set const ordsucc : set set term nat_p = \x:set.!p:set prop.p Empty -> (!y:set.p y -> p (ordsucc y)) -> p x axiom In_0_1: Empty iIn ordsucc Empty axiom ordsuccI1: !x:set.Subq x (ordsucc x) claim !x:set.nat_p x -> Empty iIn ordsucc x