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 const ordinal : set prop const ordsucc : set set axiom ordinal_ordsucc_In_Subq: !x:set.ordinal x -> !y:set.y iIn x -> Subq (ordsucc y) x lemma !x:set.!y:set.ordinal x -> y iIn x -> Subq (ordsucc y) x -> ordsucc y iIn ordsucc x claim !x:set.ordinal x -> !y:set.y iIn x -> ordsucc y iIn ordsucc x