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