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 SingE: !x:set.!y:set.y iIn Sing x -> y = x const Empty : set const ordsucc : set set axiom neq_0_2: Empty != ordsucc (ordsucc Empty) hyp TransSet (Sing (ordsucc (ordsucc Empty))) claim ~ Empty iIn Sing (ordsucc (ordsucc Empty))