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 ordsucc : set set axiom ordsuccI1: !x:set.Subq x (ordsucc x) axiom set_ext: !x:set.!y:set.Subq x y -> Subq y x -> x = y const ordinal : set prop axiom ordinal_In_Or_Subq: !x:set.!y:set.ordinal x -> ordinal y -> x iIn y | Subq y x const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 lemma !x:set.!y:set.ordinal x -> ordinal y -> Subq x y -> x iIn ordsucc y -> x <= y lemma !x:set.!y:set.Subq x y -> Subq y x -> x = y -> x iIn ordsucc y claim !x:set.!y:set.ordinal x -> ordinal y -> Subq x y -> x <= y