const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const Sing : set set axiom SingI: !x:set.x iIn Sing x axiom SingE: !x:set.!y:set.y iIn Sing x -> y = x const ordsucc : set set const Empty : set lemma Sing (ordsucc (ordsucc Empty)) iIn Sing (Sing (ordsucc Empty)) -> ~ ordsucc Empty iIn Sing (ordsucc (ordsucc Empty)) claim ~ Sing (ordsucc (ordsucc Empty)) iIn Sing (Sing (ordsucc Empty))