const binunion : set set set const Sing : set set term ordsucc = \x:set.binunion x (Sing x) const In : set set prop term iIn = In infix iIn 2000 2000 axiom SingE: !x:set.!y:set.y iIn Sing x -> y = x axiom binunionE: !x:set.!y:set.!z:set.z iIn binunion x y -> z iIn x | z iIn y claim !x:set.!y:set.y iIn ordsucc x -> y iIn x | y = x