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 Sing : set set axiom SingI: !x:set.x iIn Sing x const Empty : set const ordsucc : set set axiom In_0_1: Empty iIn ordsucc Empty lemma TransSet (Sing (ordsucc Empty)) -> ~ Empty iIn Sing (ordsucc Empty) claim ~ TransSet (Sing (ordsucc Empty))