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 term nIn = \x:set.\y:set.~ x 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 ordsuccI1: !x:set.Subq x (ordsucc x) var x:set var y:set hyp !z:set.z iIn x -> ordsucc z iIn ordsucc x hyp y iIn x claim ordsucc y iIn ordsucc x -> ordsucc y iIn ordsucc (ordsucc x)