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 SingI: !x:set.x iIn Sing x axiom binunionI2: !x:set.!y:set.!z:set.z iIn y -> z iIn binunion x y claim !x:set.x iIn ordsucc x