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 term nIn = \x:set.\y:set.~ x iIn y const Empty : set axiom EmptyE: !x:set.nIn x Empty axiom FalseE: ~ False const binunion : set set set axiom binunionE: !x:set.!y:set.!z:set.z iIn binunion x y -> z iIn x | z iIn y axiom binunionI2: !x:set.!y:set.!z:set.z iIn y -> z iIn binunion x y axiom set_ext: !x:set.!y:set.Subq x y -> Subq y x -> x = y claim !x:set.binunion Empty x = x