const binunion : set set set const Repl : set (set set) set const Inj0 : set set const Inj1 : set set term setsum = \x:set.\y:set.binunion (Repl x Inj0) (Repl y Inj1) const In : set set prop term iIn = In infix iIn 2000 2000 axiom ReplE: !x:set.!f:set set.!y:set.y iIn Repl x f -> ?z:set.z iIn x & y = f z axiom binunionE: !x:set.!y:set.!z:set.z iIn binunion x y -> z iIn x | z iIn y claim !x:set.!y:set.!z:set.z iIn setsum x y -> (?w:set.w iIn x & z = Inj0 w) | ?w:set.w iIn y & z = Inj1 w