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 TransSet = \x:set.!y:set.y iIn x -> Subq y x const omega : set const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x axiom nat_p_trans: !x:set.nat_p x -> !y:set.y iIn x -> nat_p y axiom nat_p_omega: !x:set.nat_p x -> x iIn omega claim !x:set.x iIn omega -> !y:set.y iIn x -> y iIn omega