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 binunion : set set set axiom binunionI1: !x:set.!y:set.!z:set.z iIn x -> z iIn binunion x y axiom binunionI2: !x:set.!y:set.!z:set.z iIn y -> z iIn binunion x y axiom binunionE: !x:set.!y:set.!z:set.z iIn binunion x y -> z iIn x | z iIn y axiom set_ext: !x:set.!y:set.Subq x y -> Subq y x -> x = y claim !x:set.!y:set.!z:set.binunion x (binunion y z) = binunion (binunion x y) z