const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y 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 ordinal : set prop axiom ordinal_TransSet: !x:set.ordinal x -> TransSet x axiom FalseE: ~ False var x:set var y:set var z:set hyp !w:set.w iIn y -> ordinal x -> ordinal w -> x iIn w | x = w | w iIn x hyp ordinal x hyp ordinal y hyp nIn x y hyp z iIn y claim ordinal z -> z iIn x