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 ordsucc : set set axiom ordsuccI1: !x:set.Subq x (ordsucc x) axiom ordsuccE: !x:set.!y:set.y iIn ordsucc x -> y iIn x | y = x claim !x:set.TransSet x -> !y:set.y iIn ordsucc x -> !z:set.z iIn y -> z iIn ordsucc x